32x=-5x^2+21

Solution for 32x=-5x^2+21 equation:

32x=-5x^2+21

We move all terms to the left:

32x-(-5x^2+21)=0

We get rid of parentheses

5x^2+32x-21=0

a = 5; b = 32; c = -21;
Δ = b2-4ac
Δ = 322-4·5·(-21)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-38}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+38}{2*5}=\frac{6}{10}
=3/5
$