4x^2+120x=3

Solution for 4x^2+120x=3 equation:

4x^2+120x=3

We move all terms to the left:

4x^2+120x-(3)=0

a = 4; b = 120; c = -3;
Δ = b2-4ac
Δ = 1202-4·4·(-3)
Δ = 14448
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:

$\sqrt{\Delta}=\sqrt{14448}=\sqrt{16*903}=\sqrt{16}*\sqrt{903}=4\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{903}}{2*4}=\frac{-120-4\sqrt{903}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{903}}{2*4}=\frac{-120+4\sqrt{903}}{8}
$