120-x^2=32+3x

Solution for 120-x^2=32+3x equation:

120-x^2=32+3x

We move all terms to the left:

120-x^2-(32+3x)=0

We add all the numbers together, and all the variables

-x^2-(3x+32)+120=0

We add all the numbers together, and all the variables

-1x^2-(3x+32)+120=0

We get rid of parentheses

-1x^2-3x-32+120=0

We add all the numbers together, and all the variables

-1x^2-3x+88=0

a = -1; b = -3; c = +88;
Δ = b2-4ac
Δ = -32-4·(-1)·88
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-19}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*-1}=\frac{22}{-2}
=-11
$