9x2+32=2(x+32)

Solution for 9x2+32=2(x+32) equation:

9x^2+32=2(x+32)

We move all terms to the left:

9x^2+32-(2(x+32))=0


We calculate terms in parentheses: -(2(x+32)), so:

2(x+32)

We multiply parentheses

2x+64

Back to the equation:

-(2x+64)


We get rid of parentheses

9x^2-2x-64+32=0

We add all the numbers together, and all the variables

9x^2-2x-32=0

a = 9; b = -2; c = -32;
Δ = b2-4ac
Δ = -22-4·9·(-32)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-34}{2*9}=\frac{-32}{18}
=-1+7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+34}{2*9}=\frac{36}{18}
=2
$