2(5x-15)=10x(x-15)

Solution for 2(5x-15)=10x(x-15) equation:

2(5x-15)=10x(x-15)

We move all terms to the left:

2(5x-15)-(10x(x-15))=0

We multiply parentheses

10x-(10x(x-15))-30=0


We calculate terms in parentheses: -(10x(x-15)), so:

10x(x-15)

We multiply parentheses

10x^2-150x

Back to the equation:

-(10x^2-150x)


We get rid of parentheses

-10x^2+10x+150x-30=0

We add all the numbers together, and all the variables

-10x^2+160x-30=0

a = -10; b = 160; c = -30;
Δ = b2-4ac
Δ = 1602-4·(-10)·(-30)
Δ = 24400
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:

$\sqrt{\Delta}=\sqrt{24400}=\sqrt{400*61}=\sqrt{400}*\sqrt{61}=20\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-20\sqrt{61}}{2*-10}=\frac{-160-20\sqrt{61}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+20\sqrt{61}}{2*-10}=\frac{-160+20\sqrt{61}}{-20}
$