4a^2-14a-30^2=0

Solution for 4a^2-14a-30^2=0 equation:

4a^2-14a-30^2=0

We add all the numbers together, and all the variables

4a^2-14a-900=0

a = 4; b = -14; c = -900;
Δ = b2-4ac
Δ = -142-4·4·(-900)
Δ = 14596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14596}=\sqrt{4*3649}=\sqrt{4}*\sqrt{3649}=2\sqrt{3649}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{3649}}{2*4}=\frac{14-2\sqrt{3649}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{3649}}{2*4}=\frac{14+2\sqrt{3649}}{8}
$