5x^2-32x-48=0

Solution for 5x^2-32x-48=0 equation:

5x^2-32x-48=0

a = 5; b = -32; c = -48;
Δ = b2-4ac
Δ = -322-4·5·(-48)
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{31}}{2*5}=\frac{32-8\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{31}}{2*5}=\frac{32+8\sqrt{31}}{10}
$