X2+7x+34=180

Solution for X2+7x+34=180 equation:

X2+7X+34=180

We move all terms to the left:

X2+7X+34-(180)=0

We add all the numbers together, and all the variables

X^2+7X-146=0

a = 1; b = 7; c = -146;
Δ = b2-4ac
Δ = 72-4·1·(-146)
Δ = 633
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{633}}{2*1}=\frac{-7-\sqrt{633}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{633}}{2*1}=\frac{-7+\sqrt{633}}{2}
$