52=2x^2-3x/2

Solution for 52=2x^2-3x/2 equation:

52=2x^2-3x/2

We move all terms to the left:

52-(2x^2-3x/2)=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x^2*2+3x+104=0

Wy multiply elements

-4x^2+3x+104=0

a = -4; b = 3; c = +104;
Δ = b2-4ac
Δ = 32-4·(-4)·104
Δ = 1673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{1673}}{2*-4}=\frac{-3-\sqrt{1673}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1673}}{2*-4}=\frac{-3+\sqrt{1673}}{-8}
$