5(2x-2)=9(x+5)x

Solution for 5(2x-2)=9(x+5)x equation:

5(2x-2)=9(x+5)x

We move all terms to the left:

5(2x-2)-(9(x+5)x)=0

We multiply parentheses

10x-(9(x+5)x)-10=0


We calculate terms in parentheses: -(9(x+5)x), so:

9(x+5)x

We multiply parentheses

9x^2+45x

Back to the equation:

-(9x^2+45x)


We get rid of parentheses

-9x^2+10x-45x-10=0

We add all the numbers together, and all the variables

-9x^2-35x-10=0

a = -9; b = -35; c = -10;
Δ = b2-4ac
Δ = -352-4·(-9)·(-10)
Δ = 865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{865}}{2*-9}=\frac{35-\sqrt{865}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{865}}{2*-9}=\frac{35+\sqrt{865}}{-18}
$