52x-2x^2=28x+54

Solution for 52x-2x^2=28x+54 equation:

52x-2x^2=28x+54

We move all terms to the left:

52x-2x^2-(28x+54)=0

We get rid of parentheses

-2x^2+52x-28x-54=0

We add all the numbers together, and all the variables

-2x^2+24x-54=0

a = -2; b = 24; c = -54;
Δ = b2-4ac
Δ = 242-4·(-2)·(-54)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-2}=\frac{-36}{-4}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-2}=\frac{-12}{-4}
=+3
$