30x-2x^2=52

Solution for 30x-2x^2=52 equation:

30x-2x^2=52

We move all terms to the left:

30x-2x^2-(52)=0

a = -2; b = 30; c = -52;
Δ = b2-4ac
Δ = 302-4·(-2)·(-52)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-22}{2*-2}=\frac{-52}{-4}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+22}{2*-2}=\frac{-8}{-4}
=+2
$