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(33+2x)(17+2x)-561=216
We move all terms to the left:
(33+2x)(17+2x)-561-(216)=0
We add all the numbers together, and all the variables
(2x+33)(2x+17)-561-216=0
We add all the numbers together, and all the variables
(2x+33)(2x+17)-777=0
We multiply parentheses ..
(+4x^2+34x+66x+561)-777=0
We get rid of parentheses
4x^2+34x+66x+561-777=0
We add all the numbers together, and all the variables
4x^2+100x-216=0
a = 4; b = 100; c = -216;
Δ = b2-4ac
Δ = 1002-4·4·(-216)
Δ = 13456
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{13456}=116$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-116}{2*4}=\frac{-216}{8} =-27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+116}{2*4}=\frac{16}{8} =2 $
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