x^2+48x-225=0

Solution for x^2+48x-225=0 equation:

x^2+48x-225=0

a = 1; b = 48; c = -225;
Δ = b2-4ac
Δ = 482-4·1·(-225)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{89}}{2*1}=\frac{-48-6\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{89}}{2*1}=\frac{-48+6\sqrt{89}}{2}
$