4x-6=-6x-6+10x^2

Solution for 4x-6=-6x-6+10x^2 equation:

4x-6=-6x-6+10x^2

We move all terms to the left:

4x-6-(-6x-6+10x^2)=0

We get rid of parentheses

-10x^2+6x+4x+6-6=0

We add all the numbers together, and all the variables

-10x^2+10x=0

a = -10; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-10)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-10}=\frac{-20}{-20}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-10}=\frac{0}{-20}
=0
$