0=-15x^2+52x-32

Solution for 0=-15x^2+52x-32 equation:

0=-15x^2+52x-32

We move all terms to the left:

0-(-15x^2+52x-32)=0

We add all the numbers together, and all the variables

-(-15x^2+52x-32)=0

We get rid of parentheses

15x^2-52x+32=0

a = 15; b = -52; c = +32;
Δ = b2-4ac
Δ = -522-4·15·32
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*15}=\frac{24}{30}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+28}{2*15}=\frac{80}{30}
=2+2/3
$