17x-(8-x)(3x+7)=91

Solution for 17x-(8-x)(3x+7)=91 equation:

17x-(8-x)(3x+7)=91

We move all terms to the left:

17x-(8-x)(3x+7)-(91)=0

We add all the numbers together, and all the variables

17x-(-1x+8)(3x+7)-91=0

We multiply parentheses ..

-(-3x^2-7x+24x+56)+17x-91=0

We get rid of parentheses

3x^2+7x-24x+17x-56-91=0

We add all the numbers together, and all the variables

3x^2-147=0

a = 3; b = 0; c = -147;
Δ = b2-4ac
Δ = 02-4·3·(-147)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*3}=\frac{42}{6}
=7
$