-4x^2+126+180=0

Solution for -4x^2+126+180=0 equation:

-4x^2+126+180=0

We add all the numbers together, and all the variables

-4x^2+306=0

a = -4; b = 0; c = +306;
Δ = b2-4ac
Δ = 02-4·(-4)·306
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{34}}{2*-4}=\frac{0-12\sqrt{34}}{-8}
=-\frac{12\sqrt{34}}{-8}
=-\frac{3\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{34}}{2*-4}=\frac{0+12\sqrt{34}}{-8}
=\frac{12\sqrt{34}}{-8}
=\frac{3\sqrt{34}}{-2}
$