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5x(x-1)=22
We move all terms to the left:
5x(x-1)-(22)=0
We multiply parentheses
5x^2-5x-22=0
a = 5; b = -5; c = -22;
Δ = b2-4ac
Δ = -52-4·5·(-22)
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*5}=\frac{5-\sqrt{465}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{465}}{2*5}=\frac{5+\sqrt{465}}{10} $
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