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x^2=8.5x+15
We move all terms to the left:
x^2-(8.5x+15)=0
We get rid of parentheses
x^2-8.5x-15=0
a = 1; b = -8.5; c = -15;
Δ = b2-4ac
Δ = -8.52-4·1·(-15)
Δ = 132.25
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{-(-8.5)-\sqrt{132.25}}{2*1}=\frac{8.5-\sqrt{132.25}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.5)+\sqrt{132.25}}{2*1}=\frac{8.5+\sqrt{132.25}}{2} $
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