2x^2+15x-23=180

Solution for 2x^2+15x-23=180 equation:

2x^2+15x-23=180

We move all terms to the left:

2x^2+15x-23-(180)=0

We add all the numbers together, and all the variables

2x^2+15x-203=0

a = 2; b = 15; c = -203;
Δ = b2-4ac
Δ = 152-4·2·(-203)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-43}{2*2}=\frac{-58}{4}
=-14+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+43}{2*2}=\frac{28}{4}
=7
$