x^2+14x-80=-3

Solution for x^2+14x-80=-3 equation:

x^2+14x-80=-3

We move all terms to the left:

x^2+14x-80-(-3)=0

We add all the numbers together, and all the variables

x^2+14x-77=0

a = 1; b = 14; c = -77;
Δ = b2-4ac
Δ = 142-4·1·(-77)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{14}}{2*1}=\frac{-14-6\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{14}}{2*1}=\frac{-14+6\sqrt{14}}{2}
$