4a^2+48a-54=0

Solution for 4a^2+48a-54=0 equation:

4a^2+48a-54=0

a = 4; b = 48; c = -54;
Δ = b2-4ac
Δ = 482-4·4·(-54)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{22}}{2*4}=\frac{-48-12\sqrt{22}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{22}}{2*4}=\frac{-48+12\sqrt{22}}{8}
$