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(10+2x)(18+2x)-180=x
We move all terms to the left:
(10+2x)(18+2x)-180-(x)=0
We add all the numbers together, and all the variables
(2x+10)(2x+18)-x-180=0
We add all the numbers together, and all the variables
-1x+(2x+10)(2x+18)-180=0
We multiply parentheses ..
(+4x^2+36x+20x+180)-1x-180=0
We get rid of parentheses
4x^2+36x+20x-1x+180-180=0
We add all the numbers together, and all the variables
4x^2+55x=0
a = 4; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·4·0
Δ = 3025
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{3025}=55$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*4}=\frac{-110}{8} =-13+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*4}=\frac{0}{8} =0 $
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