2x^2+19x+24=255

Solution for 2x^2+19x+24=255 equation:

2x^2+19x+24=255

We move all terms to the left:

2x^2+19x+24-(255)=0

We add all the numbers together, and all the variables

2x^2+19x-231=0

a = 2; b = 19; c = -231;
Δ = b2-4ac
Δ = 192-4·2·(-231)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-47}{2*2}=\frac{-66}{4}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+47}{2*2}=\frac{28}{4}
=7
$