48x-7x^2+63=0

Solution for 48x-7x^2+63=0 equation:

48x-7x^2+63=0

a = -7; b = 48; c = +63;
Δ = b2-4ac
Δ = 482-4·(-7)·63
Δ = 4068
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:

$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{113}}{2*-7}=\frac{-48-6\sqrt{113}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{113}}{2*-7}=\frac{-48+6\sqrt{113}}{-14}
$