10(10+8)=9x(9x+11x)

Solution for 10(10+8)=9x(9x+11x) equation:

10(10+8)=9x(9x+11x)

We move all terms to the left:

10(10+8)-(9x(9x+11x))=0

We add all the numbers together, and all the variables

-(9x(+20x))+1018=0


We calculate terms in parentheses: -(9x(+20x)), so:

9x(+20x)

We multiply parentheses

180x^2

Back to the equation:

-(180x^2)


a = -180; b = 0; c = +1018;
Δ = b2-4ac
Δ = 02-4·(-180)·1018
Δ = 732960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{732960}=\sqrt{144*5090}=\sqrt{144}*\sqrt{5090}=12\sqrt{5090}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5090}}{2*-180}=\frac{0-12\sqrt{5090}}{-360}
=-\frac{12\sqrt{5090}}{-360}
=-\frac{\sqrt{5090}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5090}}{2*-180}=\frac{0+12\sqrt{5090}}{-360}
=\frac{12\sqrt{5090}}{-360}
=\frac{\sqrt{5090}}{-30}
$