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x^2-11x+30.25=34.25
We move all terms to the left:
x^2-11x+30.25-(34.25)=0
We add all the numbers together, and all the variables
x^2-11x-4=0
a = 1; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·1·(-4)
Δ = 137
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{-(-11)-\sqrt{137}}{2*1}=\frac{11-\sqrt{137}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{137}}{2*1}=\frac{11+\sqrt{137}}{2} $
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