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5x^2=11x-2
We move all terms to the left:
5x^2-(11x-2)=0
We get rid of parentheses
5x^2-11x+2=0
a = 5; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·5·2
Δ = 81
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*5}=\frac{2}{10} =1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*5}=\frac{20}{10} =2 $
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