X^2-10x-53=0

Solution for X^2-10x-53=0 equation:

X^2-10X-53=0

a = 1; b = -10; c = -53;
Δ = b2-4ac
Δ = -102-4·1·(-53)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{78}}{2*1}=\frac{10-2\sqrt{78}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{78}}{2*1}=\frac{10+2\sqrt{78}}{2}
$