2x^2-12x-16=-6x^2+60x-144

Solution for 2x^2-12x-16=-6x^2+60x-144 equation:

2x^2-12x-16=-6x^2+60x-144

We move all terms to the left:

2x^2-12x-16-(-6x^2+60x-144)=0

We get rid of parentheses

2x^2+6x^2-60x-12x+144-16=0

We add all the numbers together, and all the variables

8x^2-72x+128=0

a = 8; b = -72; c = +128;
Δ = b2-4ac
Δ = -722-4·8·128
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{17}}{2*8}=\frac{72-8\sqrt{17}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{17}}{2*8}=\frac{72+8\sqrt{17}}{16}
$