4+14x+x^2=180

Solution for 4+14x+x^2=180 equation:

4+14x+x^2=180

We move all terms to the left:

4+14x+x^2-(180)=0

We add all the numbers together, and all the variables

x^2+14x-176=0

a = 1; b = 14; c = -176;
Δ = b2-4ac
Δ = 142-4·1·(-176)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-30}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+30}{2*1}=\frac{16}{2}
=8
$