-3x2+2x-16=2x2+2x-52

Solution for -3x2+2x-16=2x2+2x-52 equation:

-3x^2+2x-16=2x^2+2x-52

We move all terms to the left:

-3x^2+2x-16-(2x^2+2x-52)=0

We get rid of parentheses

-3x^2-2x^2+2x-2x+52-16=0

We add all the numbers together, and all the variables

-5x^2+36=0

a = -5; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-5)·36
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*-5}=\frac{0-12\sqrt{5}}{-10}
=-\frac{12\sqrt{5}}{-10}
=-\frac{6\sqrt{5}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-5}=\frac{0+12\sqrt{5}}{-10}
=\frac{12\sqrt{5}}{-10}
=\frac{6\sqrt{5}}{-5}
$