Solve 98x+102.6/9-0*3x+81=x^2+8x

$$9 \frac{ 8x+102.6 }{ 9-0 \cdot 3x } +81 = { x }^{ 2 } +8x$$

Solve for x

$$x = \frac{3 \sqrt{510}}{5} \approx 13.549907749$$

$$x = -\frac{3 \sqrt{510}}{5} \approx -13.549907749$$

Steps by Finding Square Root

Multiply both sides of the equation by 9.

$$81\times \frac{8x+102.6}{9-0\times 3x}+729=9x^{2}+72x$$

Multiply 0 and 3 to get 0.

$$81\times \frac{8x+102.6}{9-0x}+729=9x^{2}+72x$$

Anything times zero gives zero.

$$81\times \frac{8x+102.6}{9-0}+729=9x^{2}+72x$$

Subtract 0 from 9 to get 9.

$$81\times \frac{8x+102.6}{9}+729=9x^{2}+72x$$

Divide each term of 8x+102.6 by 9 to get \frac{8}{9}x+11.4.

$$81\left(\frac{8}{9}x+11.4\right)+729=9x^{2}+72x$$

Use the distributive property to multiply 81 by \frac{8}{9}x+11.4.

$$72x+923.4+729=9x^{2}+72x$$

Add 923.4 and 729 to get 1652.4.

$$72x+1652.4=9x^{2}+72x$$

Subtract 9x^{2} from both sides.

$$72x+1652.4-9x^{2}=72x$$

Subtract 72x from both sides.

$$72x+1652.4-9x^{2}-72x=0$$

Combine 72x and -72x to get 0.

$$1652.4-9x^{2}=0$$

Subtract 1652.4 from both sides. Anything subtracted from zero gives its negation.

$$-9x^{2}=-1652.4$$

Divide both sides by -9.

$$x^{2}=\frac{-1652.4}{-9}$$

Expand \frac{-1652.4}{-9} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{-16524}{-90}$$

Reduce the fraction \frac{-16524}{-90} to lowest terms by extracting and canceling out -18.

$$x^{2}=\frac{918}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{510}}{5} x=-\frac{3\sqrt{510}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 9.

$$81\times \frac{8x+102.6}{9-0\times 3x}+729=9x^{2}+72x$$

Multiply 0 and 3 to get 0.

$$81\times \frac{8x+102.6}{9-0x}+729=9x^{2}+72x$$

Anything times zero gives zero.

$$81\times \frac{8x+102.6}{9-0}+729=9x^{2}+72x$$

Subtract 0 from 9 to get 9.

$$81\times \frac{8x+102.6}{9}+729=9x^{2}+72x$$

Divide each term of 8x+102.6 by 9 to get \frac{8}{9}x+11.4.

$$81\left(\frac{8}{9}x+11.4\right)+729=9x^{2}+72x$$

Use the distributive property to multiply 81 by \frac{8}{9}x+11.4.

$$72x+923.4+729=9x^{2}+72x$$

Add 923.4 and 729 to get 1652.4.

$$72x+1652.4=9x^{2}+72x$$

Subtract 9x^{2} from both sides.

$$72x+1652.4-9x^{2}=72x$$

Subtract 72x from both sides.

$$72x+1652.4-9x^{2}-72x=0$$

Combine 72x and -72x to get 0.

$$1652.4-9x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-9x^{2}+1652.4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 1652.4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 1652.4}}{2\left(-9\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 1652.4}}{2\left(-9\right)}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36\times 1652.4}}{2\left(-9\right)}$$

Multiply 36 times 1652.4.

$$x=\frac{0±\sqrt{59486.4}}{2\left(-9\right)}$$

Take the square root of 59486.4.

$$x=\frac{0±\frac{54\sqrt{510}}{5}}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{0±\frac{54\sqrt{510}}{5}}{-18}$$

Now solve the equation x=\frac{0±\frac{54\sqrt{510}}{5}}{-18} when ± is plus.

$$x=-\frac{3\sqrt{510}}{5}$$

Now solve the equation x=\frac{0±\frac{54\sqrt{510}}{5}}{-18} when ± is minus.

$$x=\frac{3\sqrt{510}}{5}$$

The equation is now solved.

$$x=-\frac{3\sqrt{510}}{5} x=\frac{3\sqrt{510}}{5}$$