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10x^2-5x=11=9x^2+x+83
We move all terms to the left:
10x^2-5x-(11)=0
a = 10; b = -5; c = -11;
Δ = b2-4ac
Δ = -52-4·10·(-11)
Δ = 465
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)-\sqrt{465}}{2*10}=\frac{5-\sqrt{465}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{465}}{2*10}=\frac{5+\sqrt{465}}{20} $
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