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x^2/2-5x=2.75
We move all terms to the left:
x^2/2-5x-(2.75)=0
We add all the numbers together, and all the variables
x^2/2-5x-2.75=0
We multiply all the terms by the denominator
x^2-5x*2-(2.75)*2=0
We add all the numbers together, and all the variables
x^2-5x*2-5.5=0
Wy multiply elements
x^2-10x-5.5=0
a = 1; b = -10; c = -5.5;
Δ = b2-4ac
Δ = -102-4·1·(-5.5)
Δ = 122
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{-(-10)-\sqrt{122}}{2*1}=\frac{10-\sqrt{122}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{122}}{2*1}=\frac{10+\sqrt{122}}{2} $
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