X2-10x=114

Solution for X2-10x=114 equation:

X2-10X=114

We move all terms to the left:

X2-10X-(114)=0

We add all the numbers together, and all the variables

X^2-10X-114=0

a = 1; b = -10; c = -114;
Δ = b2-4ac
Δ = -102-4·1·(-114)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{139}}{2*1}=\frac{10-2\sqrt{139}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{139}}{2*1}=\frac{10+2\sqrt{139}}{2}
$