0=4x^2-10x-30

Solution for 0=4x^2-10x-30 equation:

0=4x^2-10x-30

We move all terms to the left:

0-(4x^2-10x-30)=0

We add all the numbers together, and all the variables

-(4x^2-10x-30)=0

We get rid of parentheses

-4x^2+10x+30=0

a = -4; b = 10; c = +30;
Δ = b2-4ac
Δ = 102-4·(-4)·30
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{145}}{2*-4}=\frac{-10-2\sqrt{145}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{145}}{2*-4}=\frac{-10+2\sqrt{145}}{-8}
$