x(4x-6)=-6x+30+12x

Solution for x(4x-6)=-6x+30+12x equation:

x(4x-6)=-6x+30+12x

We move all terms to the left:

x(4x-6)-(-6x+30+12x)=0

We add all the numbers together, and all the variables

x(4x-6)-(6x+30)=0

We multiply parentheses

4x^2-6x-(6x+30)=0

We get rid of parentheses

4x^2-6x-6x-30=0

We add all the numbers together, and all the variables

4x^2-12x-30=0

a = 4; b = -12; c = -30;
Δ = b2-4ac
Δ = -122-4·4·(-30)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{39}}{2*4}=\frac{12-4\sqrt{39}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{39}}{2*4}=\frac{12+4\sqrt{39}}{8}
$