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(2x+18)(2x+9)=400
We move all terms to the left:
(2x+18)(2x+9)-(400)=0
We multiply parentheses ..
(+4x^2+18x+36x+162)-400=0
We get rid of parentheses
4x^2+18x+36x+162-400=0
We add all the numbers together, and all the variables
4x^2+54x-238=0
a = 4; b = 54; c = -238;
Δ = b2-4ac
Δ = 542-4·4·(-238)
Δ = 6724
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{6724}=82$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-82}{2*4}=\frac{-136}{8} =-17 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+82}{2*4}=\frac{28}{8} =3+1/2 $
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