2x^2+19x+45=15

Solution for 2x^2+19x+45=15 equation:

2x^2+19x+45=15

We move all terms to the left:

2x^2+19x+45-(15)=0

We add all the numbers together, and all the variables

2x^2+19x+30=0

a = 2; b = 19; c = +30;
Δ = b2-4ac
Δ = 192-4·2·30
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*2}=\frac{-8}{4}
=-2
$