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y^2=11y+30
We move all terms to the left:
y^2-(11y+30)=0
We get rid of parentheses
y^2-11y-30=0
a = 1; b = -11; c = -30;
Δ = b2-4ac
Δ = -112-4·1·(-30)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{241}}{2*1}=\frac{11-\sqrt{241}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{241}}{2*1}=\frac{11+\sqrt{241}}{2} $
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