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(3x+17)(7x-39)=180
We move all terms to the left:
(3x+17)(7x-39)-(180)=0
We multiply parentheses ..
(+21x^2-117x+119x-663)-180=0
We get rid of parentheses
21x^2-117x+119x-663-180=0
We add all the numbers together, and all the variables
21x^2+2x-843=0
a = 21; b = 2; c = -843;
Δ = b2-4ac
Δ = 22-4·21·(-843)
Δ = 70816
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{70816}=\sqrt{16*4426}=\sqrt{16}*\sqrt{4426}=4\sqrt{4426}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{4426}}{2*21}=\frac{-2-4\sqrt{4426}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{4426}}{2*21}=\frac{-2+4\sqrt{4426}}{42} $
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