x2+5x=55

Solution for x2+5x=55 equation:

x2+5x=55

We move all terms to the left:

x2+5x-(55)=0

We add all the numbers together, and all the variables

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}
$