5x^2+22x-75=0

Solution for 5x^2+22x-75=0 equation:

5x^2+22x-75=0

a = 5; b = 22; c = -75;
Δ = b2-4ac
Δ = 222-4·5·(-75)
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{-(22)-8\sqrt{31}}{2*5}=\frac{-22-8\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8\sqrt{31}}{2*5}=\frac{-22+8\sqrt{31}}{10}
$