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(7x+1)(x-1)+15x+17+20x-4=180
We move all terms to the left:
(7x+1)(x-1)+15x+17+20x-4-(180)=0
We add all the numbers together, and all the variables
35x+(7x+1)(x-1)-167=0
We multiply parentheses ..
(+7x^2-7x+x-1)+35x-167=0
We get rid of parentheses
7x^2-7x+x+35x-1-167=0
We add all the numbers together, and all the variables
7x^2+29x-168=0
a = 7; b = 29; c = -168;
Δ = b2-4ac
Δ = 292-4·7·(-168)
Δ = 5545
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{-(29)-\sqrt{5545}}{2*7}=\frac{-29-\sqrt{5545}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{5545}}{2*7}=\frac{-29+\sqrt{5545}}{14} $
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