52=2x2+3x+8

Solution for 52=2x2+3x+8 equation:

52=2x^2+3x+8

We move all terms to the left:

52-(2x^2+3x+8)=0

We get rid of parentheses

-2x^2-3x-8+52=0

We add all the numbers together, and all the variables

-2x^2-3x+44=0

a = -2; b = -3; c = +44;
Δ = b2-4ac
Δ = -32-4·(-2)·44
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-19}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*-2}=\frac{22}{-4}
=-5+1/2
$