2x2=19x+33

Solution for 2x2=19x+33 equation:

2x^2=19x+33

We move all terms to the left:

2x^2-(19x+33)=0

We get rid of parentheses

2x^2-19x-33=0

a = 2; b = -19; c = -33;
Δ = b2-4ac
Δ = -192-4·2·(-33)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-25}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+25}{2*2}=\frac{44}{4}
=11
$