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2.5x^2-5.5x+53=52
We move all terms to the left:
2.5x^2-5.5x+53-(52)=0
We add all the numbers together, and all the variables
2.5x^2-5.5x+1=0
a = 2.5; b = -5.5; c = +1;
Δ = b2-4ac
Δ = -5.52-4·2.5·1
Δ = 20.25
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{-(-5.5)-\sqrt{20.25}}{2*2.5}=\frac{5.5-\sqrt{20.25}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{20.25}}{2*2.5}=\frac{5.5+\sqrt{20.25}}{5} $
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