80+2x^2+3x=180

Solution for 80+2x^2+3x=180 equation:

80+2x^2+3x=180

We move all terms to the left:

80+2x^2+3x-(180)=0

We add all the numbers together, and all the variables

2x^2+3x-100=0

a = 2; b = 3; c = -100;
Δ = b2-4ac
Δ = 32-4·2·(-100)
Δ = 809
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{-(3)-\sqrt{809}}{2*2}=\frac{-3-\sqrt{809}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{809}}{2*2}=\frac{-3+\sqrt{809}}{4}
$