X(4x-3)=63

Solution for X(4x-3)=63 equation:

X(4X-3)=63

We move all terms to the left:

X(4X-3)-(63)=0

We multiply parentheses

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}
$