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(x+11)(2x+5)=117^2
We move all terms to the left:
(x+11)(2x+5)-(117^2)=0
We add all the numbers together, and all the variables
(x+11)(2x+5)-13689=0
We multiply parentheses ..
(+2x^2+5x+22x+55)-13689=0
We get rid of parentheses
2x^2+5x+22x+55-13689=0
We add all the numbers together, and all the variables
2x^2+27x-13634=0
a = 2; b = 27; c = -13634;
Δ = b2-4ac
Δ = 272-4·2·(-13634)
Δ = 109801
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{-(27)-\sqrt{109801}}{2*2}=\frac{-27-\sqrt{109801}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{109801}}{2*2}=\frac{-27+\sqrt{109801}}{4} $
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