4x^2+3x-63=0

Solution for 4x^2+3x-63=0 equation:

4x^2+3x-63=0

a = 4; b = 3; c = -63;
Δ = b2-4ac
Δ = 32-4·4·(-63)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{113}}{2*4}=\frac{-3-3\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{113}}{2*4}=\frac{-3+3\sqrt{113}}{8}
$