x^2-4x-75=0

Solution for x^2-4x-75=0 equation:

x^2-4x-75=0

a = 1; b = -4; c = -75;
Δ = b2-4ac
Δ = -42-4·1·(-75)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{79}}{2*1}=\frac{4-2\sqrt{79}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{79}}{2*1}=\frac{4+2\sqrt{79}}{2}
$