180=x^2-8+(-8x+1)+(-7x)

Solution for 180=x^2-8+(-8x+1)+(-7x) equation:

180=x^2-8+(-8x+1)+(-7x)

We move all terms to the left:

180-(x^2-8+(-8x+1)+(-7x))=0


We calculate terms in parentheses: -(x^2-8+(-8x+1)+(-7x)), so:

x^2-8+(-8x+1)+(-7x)

determiningTheFunctionDomain
x^2+(-8x+1)+(-7x)-8

We get rid of parentheses

x^2-8x-7x+1-8

We add all the numbers together, and all the variables

x^2-15x-7

Back to the equation:

-(x^2-15x-7)


We get rid of parentheses

-x^2+15x+7+180=0

We add all the numbers together, and all the variables

-1x^2+15x+187=0

a = -1; b = 15; c = +187;
Δ = b2-4ac
Δ = 152-4·(-1)·187
Δ = 973
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{973}}{2*-1}=\frac{-15-\sqrt{973}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{973}}{2*-1}=\frac{-15+\sqrt{973}}{-2}
$