(14+x)(48x)=63*63

Solution for (14+x)(48x)=63*63 equation:

(14+x)(48x)=63*63

We move all terms to the left:

(14+x)(48x)-(63*63)=0

We add all the numbers together, and all the variables

(x+14)48x-3969=0

We multiply parentheses

48x^2+672x-3969=0

a = 48; b = 672; c = -3969;
Δ = b2-4ac
Δ = 6722-4·48·(-3969)
Δ = 1213632
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:

$\sqrt{\Delta}=\sqrt{1213632}=\sqrt{28224*43}=\sqrt{28224}*\sqrt{43}=168\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(672)-168\sqrt{43}}{2*48}=\frac{-672-168\sqrt{43}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(672)+168\sqrt{43}}{2*48}=\frac{-672+168\sqrt{43}}{96}
$