x^2+4x-7+74=180

Solution for x^2+4x-7+74=180 equation:

x^2+4x-7+74=180

We move all terms to the left:

x^2+4x-7+74-(180)=0

We add all the numbers together, and all the variables

x^2+4x-113=0

a = 1; b = 4; c = -113;
Δ = b2-4ac
Δ = 42-4·1·(-113)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{13}}{2*1}=\frac{-4-6\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{13}}{2*1}=\frac{-4+6\sqrt{13}}{2}
$