X2+8x+14=180

Solution for X2+8x+14=180 equation:

X2+8X+14=180

We move all terms to the left:

X2+8X+14-(180)=0

We add all the numbers together, and all the variables

X^2+8X-166=0

a = 1; b = 8; c = -166;
Δ = b2-4ac
Δ = 82-4·1·(-166)
Δ = 728
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:

$\sqrt{\Delta}=\sqrt{728}=\sqrt{4*182}=\sqrt{4}*\sqrt{182}=2\sqrt{182}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{182}}{2*1}=\frac{-8-2\sqrt{182}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{182}}{2*1}=\frac{-8+2\sqrt{182}}{2}
$