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(5x-22)(8x=46)
We move all terms to the left:
(5x-22)(8x-(46))=0
We multiply parentheses ..
(+40x^2-230x-176x+1012)=0
We get rid of parentheses
40x^2-230x-176x+1012=0
We add all the numbers together, and all the variables
40x^2-406x+1012=0
a = 40; b = -406; c = +1012;
Δ = b2-4ac
Δ = -4062-4·40·1012
Δ = 2916
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{2916}=54$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-406)-54}{2*40}=\frac{352}{80} =4+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-406)+54}{2*40}=\frac{460}{80} =5+3/4 $
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