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(38-2x)(22-2x)=420
We move all terms to the left:
(38-2x)(22-2x)-(420)=0
We add all the numbers together, and all the variables
(-2x+38)(-2x+22)-420=0
We multiply parentheses ..
(+4x^2-44x-76x+836)-420=0
We get rid of parentheses
4x^2-44x-76x+836-420=0
We add all the numbers together, and all the variables
4x^2-120x+416=0
a = 4; b = -120; c = +416;
Δ = b2-4ac
Δ = -1202-4·4·416
Δ = 7744
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{7744}=88$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-88}{2*4}=\frac{32}{8} =4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+88}{2*4}=\frac{208}{8} =26 $
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