32-3x^2=10x

Solution for 32-3x^2=10x equation:

32-3x^2=10x

We move all terms to the left:

32-3x^2-(10x)=0

a = -3; b = -10; c = +32;
Δ = b2-4ac
Δ = -102-4·(-3)·32
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{-(-10)-22}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*-3}=\frac{32}{-6}
=-5+1/3
$