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(X-1)(X-1.5)=24
We move all terms to the left:
(X-1)(X-1.5)-(24)=0
We multiply parentheses ..
(+X^2-1.5X-1X+1.5)-24=0
We get rid of parentheses
X^2-1.5X-1X+1.5-24=0
We add all the numbers together, and all the variables
X^2-2.5X-22.5=0
a = 1; b = -2.5; c = -22.5;
Δ = b2-4ac
Δ = -2.52-4·1·(-22.5)
Δ = 96.25
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{-(-2.5)-\sqrt{96.25}}{2*1}=\frac{2.5-\sqrt{96.25}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{96.25}}{2*1}=\frac{2.5+\sqrt{96.25}}{2} $
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