54=2x2-3x

Solution for 54=2x2-3x equation:

54=2x^2-3x

We move all terms to the left:

54-(2x^2-3x)=0

We get rid of parentheses

-2x^2+3x+54=0

a = -2; b = 3; c = +54;
Δ = b2-4ac
Δ = 32-4·(-2)·54
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*-2}=\frac{18}{-4}
=-4+1/2
$