x^2+7x=49=-11

Solution for x^2+7x=49=-11 equation:

x^2+7x=49=-11

We move all terms to the left:

x^2+7x-(49)=0

a = 1; b = 7; c = -49;
Δ = b2-4ac
Δ = 72-4·1·(-49)
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{-(7)-7\sqrt{5}}{2*1}=\frac{-7-7\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{5}}{2*1}=\frac{-7+7\sqrt{5}}{2}
$