2x^2+14x+45=180

Solution for 2x^2+14x+45=180 equation:

2x^2+14x+45=180

We move all terms to the left:

2x^2+14x+45-(180)=0

We add all the numbers together, and all the variables

2x^2+14x-135=0

a = 2; b = 14; c = -135;
Δ = b2-4ac
Δ = 142-4·2·(-135)
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{319}}{2*2}=\frac{-14-2\sqrt{319}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{319}}{2*2}=\frac{-14+2\sqrt{319}}{4}
$