0=4x^2-24x-30

Solution for 0=4x^2-24x-30 equation:

0=4x^2-24x-30

We move all terms to the left:

0-(4x^2-24x-30)=0

We add all the numbers together, and all the variables

-(4x^2-24x-30)=0

We get rid of parentheses

-4x^2+24x+30=0

a = -4; b = 24; c = +30;
Δ = b2-4ac
Δ = 242-4·(-4)·30
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{66}}{2*-4}=\frac{-24-4\sqrt{66}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{66}}{2*-4}=\frac{-24+4\sqrt{66}}{-8}
$