Finite Math Examples

$0 = 3900 x + 326 - 20.22 x^{2}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $3900 x$ from both sides of the equation.

$- 3900 x = 326 - 20.22 x^{2}$

Step 1.2

Subtract $326$ from both sides of the equation.

$- 3900 x - 326 = - 20.22 x^{2}$

Step 1.3

Add $20.22 x^{2}$ to both sides of the equation.

$- 3900 x - 326 + 20.22 x^{2} = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 20.22$ , $b = - 3900$ , and $c = - 326$ into the quadratic formula and solve for $x$ .

$\frac{3900 \pm \sqrt{{(- 3900)}^{2} - 4 \cdot (20.22 \cdot - 326)}}{2 \cdot 20.22}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 3900$ to the power of $2$ .

$x = \frac{3900 \pm \sqrt{15210000 - 4 \cdot 20.22 \cdot - 326}}{2 \cdot 20.22}$

Step 4.1.2

Multiply $- 4 \cdot 20.22 \cdot - 326$ .

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Step 4.1.2.1

Multiply $- 4$ by $20.22$ .

$x = \frac{3900 \pm \sqrt{15210000 - 80.88 \cdot - 326}}{2 \cdot 20.22}$

Step 4.1.2.2

Multiply $- 80.88$ by $- 326$ .

$x = \frac{3900 \pm \sqrt{15210000 + 26366.88}}{2 \cdot 20.22}$

Step 4.1.3

Add $15210000$ and $26366.88$ .

$x = \frac{3900 \pm \sqrt{15236366.88}}{2 \cdot 20.22}$

Step 4.2

Multiply $2$ by $20.22$ .

$x = \frac{3900 \pm \sqrt{15236366.88}}{40.44}$

Step 4.3

Simplify $\frac{3900 \pm \sqrt{15236366.88}}{40.44}$ .

$x = \frac{97500 \pm 25 \sqrt{15236366.88}}{1011}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{97500 \pm 25 \sqrt{15236366.88}}{1011}$

Decimal Form:

$x = 192.96189182 \dots, - 0.08355354 \dots$