52x-0.8x^2=600

Solution for 52x-0.8x^2=600 equation:

52x-0.8x^2=600

We move all terms to the left:

52x-0.8x^2-(600)=0

a = -0.8; b = 52; c = -600;
Δ = b2-4ac
Δ = 522-4·(-0.8)·(-600)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-28}{2*-0.8}=\frac{-80}{-1.6}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+28}{2*-0.8}=\frac{-24}{-1.6}
=+15
$