10x^2-18x-52=0

Solution for 10x^2-18x-52=0 equation:

10x^2-18x-52=0

a = 10; b = -18; c = -52;
Δ = b2-4ac
Δ = -182-4·10·(-52)
Δ = 2404
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:

$\sqrt{\Delta}=\sqrt{2404}=\sqrt{4*601}=\sqrt{4}*\sqrt{601}=2\sqrt{601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{601}}{2*10}=\frac{18-2\sqrt{601}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{601}}{2*10}=\frac{18+2\sqrt{601}}{20}
$