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(2x+7)(9x-3)=180
We move all terms to the left:
(2x+7)(9x-3)-(180)=0
We multiply parentheses ..
(+18x^2-6x+63x-21)-180=0
We get rid of parentheses
18x^2-6x+63x-21-180=0
We add all the numbers together, and all the variables
18x^2+57x-201=0
a = 18; b = 57; c = -201;
Δ = b2-4ac
Δ = 572-4·18·(-201)
Δ = 17721
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17721}=\sqrt{9*1969}=\sqrt{9}*\sqrt{1969}=3\sqrt{1969}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{1969}}{2*18}=\frac{-57-3\sqrt{1969}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{1969}}{2*18}=\frac{-57+3\sqrt{1969}}{36} $
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