X2-10x=1190

Solution for X2-10x=1190 equation:

X2-10X=1190

We move all terms to the left:

X2-10X-(1190)=0

We add all the numbers together, and all the variables

X^2-10X-1190=0

a = 1; b = -10; c = -1190;
Δ = b2-4ac
Δ = -102-4·1·(-1190)
Δ = 4860
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:

$\sqrt{\Delta}=\sqrt{4860}=\sqrt{324*15}=\sqrt{324}*\sqrt{15}=18\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-18\sqrt{15}}{2*1}=\frac{10-18\sqrt{15}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+18\sqrt{15}}{2*1}=\frac{10+18\sqrt{15}}{2}
$