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(12+2x)(15+2x)=270
We move all terms to the left:
(12+2x)(15+2x)-(270)=0
We add all the numbers together, and all the variables
(2x+12)(2x+15)-270=0
We multiply parentheses ..
(+4x^2+30x+24x+180)-270=0
We get rid of parentheses
4x^2+30x+24x+180-270=0
We add all the numbers together, and all the variables
4x^2+54x-90=0
a = 4; b = 54; c = -90;
Δ = b2-4ac
Δ = 542-4·4·(-90)
Δ = 4356
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{4356}=66$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-66}{2*4}=\frac{-120}{8} =-15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+66}{2*4}=\frac{12}{8} =1+1/2 $
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