X^2+48x-9=0

Solution for X^2+48x-9=0 equation:

X^2+48X-9=0

a = 1; b = 48; c = -9;
Δ = b2-4ac
Δ = 482-4·1·(-9)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{65}}{2*1}=\frac{-48-6\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{65}}{2*1}=\frac{-48+6\sqrt{65}}{2}
$