15x(10+5x)=20x-10

Solution for 15x(10+5x)=20x-10 equation:

15x(10+5x)=20x-10

We move all terms to the left:

15x(10+5x)-(20x-10)=0

We add all the numbers together, and all the variables

15x(5x+10)-(20x-10)=0

We multiply parentheses

75x^2+150x-(20x-10)=0

We get rid of parentheses

75x^2+150x-20x+10=0

We add all the numbers together, and all the variables

75x^2+130x+10=0

a = 75; b = 130; c = +10;
Δ = b2-4ac
Δ = 1302-4·75·10
Δ = 13900
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:

$\sqrt{\Delta}=\sqrt{13900}=\sqrt{100*139}=\sqrt{100}*\sqrt{139}=10\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-10\sqrt{139}}{2*75}=\frac{-130-10\sqrt{139}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+10\sqrt{139}}{2*75}=\frac{-130+10\sqrt{139}}{150}
$