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(27+2x)(18+2x)=972
We move all terms to the left:
(27+2x)(18+2x)-(972)=0
We add all the numbers together, and all the variables
(2x+27)(2x+18)-972=0
We multiply parentheses ..
(+4x^2+36x+54x+486)-972=0
We get rid of parentheses
4x^2+36x+54x+486-972=0
We add all the numbers together, and all the variables
4x^2+90x-486=0
a = 4; b = 90; c = -486;
Δ = b2-4ac
Δ = 902-4·4·(-486)
Δ = 15876
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{15876}=126$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-126}{2*4}=\frac{-216}{8} =-27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+126}{2*4}=\frac{36}{8} =4+1/2 $
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