2x+6(3x-5)=6x^2-10x-30

Solution for 2x+6(3x-5)=6x^2-10x-30 equation:

2x+6(3x-5)=6x^2-10x-30

We move all terms to the left:

2x+6(3x-5)-(6x^2-10x-30)=0

We multiply parentheses

2x+18x-(6x^2-10x-30)-30=0

We get rid of parentheses

-6x^2+2x+18x+10x+30-30=0

We add all the numbers together, and all the variables

-6x^2+30x=0

a = -6; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-6)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-6}=\frac{0}{-12}
=0
$