x^2+7x=65

Solution for x^2+7x=65 equation:

x^2+7x=65

We move all terms to the left:

x^2+7x-(65)=0

a = 1; b = 7; c = -65;
Δ = b2-4ac
Δ = 72-4·1·(-65)
Δ = 309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{309}}{2*1}=\frac{-7-\sqrt{309}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{309}}{2*1}=\frac{-7+\sqrt{309}}{2}
$