6x+4+2x^2=180

Solution for 6x+4+2x^2=180 equation:

6x+4+2x^2=180

We move all terms to the left:

6x+4+2x^2-(180)=0

We add all the numbers together, and all the variables

2x^2+6x-176=0

a = 2; b = 6; c = -176;
Δ = b2-4ac
Δ = 62-4·2·(-176)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-38}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+38}{2*2}=\frac{32}{4}
=8
$