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10x^2-9x=11
We move all terms to the left:
10x^2-9x-(11)=0
a = 10; b = -9; c = -11;
Δ = b2-4ac
Δ = -92-4·10·(-11)
Δ = 521
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{-(-9)-\sqrt{521}}{2*10}=\frac{9-\sqrt{521}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{521}}{2*10}=\frac{9+\sqrt{521}}{20} $
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