15-x(10+15x)=20x-10

Solution for 15-x(10+15x)=20x-10 equation:

15-x(10+15x)=20x-10

We move all terms to the left:

15-x(10+15x)-(20x-10)=0

We add all the numbers together, and all the variables

-x(15x+10)-(20x-10)+15=0

We multiply parentheses

-15x^2-10x-(20x-10)+15=0

We get rid of parentheses

-15x^2-10x-20x+10+15=0

We add all the numbers together, and all the variables

-15x^2-30x+25=0

a = -15; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·(-15)·25
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-20\sqrt{6}}{2*-15}=\frac{30-20\sqrt{6}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+20\sqrt{6}}{2*-15}=\frac{30+20\sqrt{6}}{-30}
$