0=4x^2+2x-30

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

0=4x^2+2x-30

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -4; b = -2; c = +30;
Δ = b2-4ac
Δ = -22-4·(-4)·30
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*-4}=\frac{24}{-8}
=-3
$