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5x(x-1)-6x=-3
We move all terms to the left:
5x(x-1)-6x-(-3)=0
We add all the numbers together, and all the variables
-6x+5x(x-1)+3=0
We multiply parentheses
5x^2-6x-5x+3=0
We add all the numbers together, and all the variables
5x^2-11x+3=0
a = 5; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·5·3
Δ = 61
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{-(-11)-\sqrt{61}}{2*5}=\frac{11-\sqrt{61}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{61}}{2*5}=\frac{11+\sqrt{61}}{10} $
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