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(x+17)(2x+1)=180
We move all terms to the left:
(x+17)(2x+1)-(180)=0
We multiply parentheses ..
(+2x^2+x+34x+17)-180=0
We get rid of parentheses
2x^2+x+34x+17-180=0
We add all the numbers together, and all the variables
2x^2+35x-163=0
a = 2; b = 35; c = -163;
Δ = b2-4ac
Δ = 352-4·2·(-163)
Δ = 2529
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-3\sqrt{281}}{2*2}=\frac{-35-3\sqrt{281}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+3\sqrt{281}}{2*2}=\frac{-35+3\sqrt{281}}{4} $
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