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(37-x)(6-x)=96
We move all terms to the left:
(37-x)(6-x)-(96)=0
We add all the numbers together, and all the variables
(-1x+37)(-1x+6)-96=0
We multiply parentheses ..
(+x^2-6x-37x+222)-96=0
We get rid of parentheses
x^2-6x-37x+222-96=0
We add all the numbers together, and all the variables
x^2-43x+126=0
a = 1; b = -43; c = +126;
Δ = b2-4ac
Δ = -432-4·1·126
Δ = 1345
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{1345}}{2*1}=\frac{43-\sqrt{1345}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{1345}}{2*1}=\frac{43+\sqrt{1345}}{2} $
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