X^2-5x=55

Solution for X^2-5x=55 equation:

X^2-5X=55

We move all terms to the left:

X^2-5X-(55)=0

a = 1; b = -5; c = -55;
Δ = b2-4ac
Δ = -52-4·1·(-55)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7\sqrt{5}}{2*1}=\frac{5-7\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7\sqrt{5}}{2*1}=\frac{5+7\sqrt{5}}{2}
$