5x^2-66x-275=0

Solution for 5x^2-66x-275=0 equation:

5x^2-66x-275=0

a = 5; b = -66; c = -275;
Δ = b2-4ac
Δ = -662-4·5·(-275)
Δ = 9856
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:

$\sqrt{\Delta}=\sqrt{9856}=\sqrt{64*154}=\sqrt{64}*\sqrt{154}=8\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-8\sqrt{154}}{2*5}=\frac{66-8\sqrt{154}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+8\sqrt{154}}{2*5}=\frac{66+8\sqrt{154}}{10}
$