7x-3+x^2+29=180

Solution for 7x-3+x^2+29=180 equation:

7x-3+x^2+29=180

We move all terms to the left:

7x-3+x^2+29-(180)=0

We add all the numbers together, and all the variables

x^2+7x-154=0

a = 1; b = 7; c = -154;
Δ = b2-4ac
Δ = 72-4·1·(-154)
Δ = 665
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{665}}{2*1}=\frac{-7-\sqrt{665}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{665}}{2*1}=\frac{-7+\sqrt{665}}{2}
$