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(2x-2.5)(x-2.5)=8.25
We move all terms to the left:
(2x-2.5)(x-2.5)-(8.25)=0
We add all the numbers together, and all the variables
(2x-2.5)(x-2.5)-8.25=0
We multiply parentheses ..
(+2x^2-5x-2.5x+6.25)-8.25=0
We get rid of parentheses
2x^2-5x-2.5x+6.25-8.25=0
We add all the numbers together, and all the variables
2x^2-7.5x-2=0
a = 2; b = -7.5; c = -2;
Δ = b2-4ac
Δ = -7.52-4·2·(-2)
Δ = 72.25
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{-(-7.5)-\sqrt{72.25}}{2*2}=\frac{7.5-\sqrt{72.25}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{72.25}}{2*2}=\frac{7.5+\sqrt{72.25}}{4} $
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