180=90+(8x-3)+(x^2+9)

Solution for 180=90+(8x-3)+(x^2+9) equation:

180=90+(8x-3)+(x^2+9)

We move all terms to the left:

180-(90+(8x-3)+(x^2+9))=0


We calculate terms in parentheses: -(90+(8x-3)+(x^2+9)), so:

90+(8x-3)+(x^2+9)

determiningTheFunctionDomain
(8x-3)+(x^2+9)+90

We get rid of parentheses

x^2+8x-3+9+90

We add all the numbers together, and all the variables

x^2+8x+96

Back to the equation:

-(x^2+8x+96)


We get rid of parentheses

-x^2-8x-96+180=0

We add all the numbers together, and all the variables

-1x^2-8x+84=0

a = -1; b = -8; c = +84;
Δ = b2-4ac
Δ = -82-4·(-1)·84
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*-1}=\frac{28}{-2}
=-14
$