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(5x-17)(4x+17)=180
We move all terms to the left:
(5x-17)(4x+17)-(180)=0
We multiply parentheses ..
(+20x^2+85x-68x-289)-180=0
We get rid of parentheses
20x^2+85x-68x-289-180=0
We add all the numbers together, and all the variables
20x^2+17x-469=0
a = 20; b = 17; c = -469;
Δ = b2-4ac
Δ = 172-4·20·(-469)
Δ = 37809
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{37809}=\sqrt{9*4201}=\sqrt{9}*\sqrt{4201}=3\sqrt{4201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{4201}}{2*20}=\frac{-17-3\sqrt{4201}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{4201}}{2*20}=\frac{-17+3\sqrt{4201}}{40} $
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