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(5x-2)(2x-1)=6
We move all terms to the left:
(5x-2)(2x-1)-(6)=0
We multiply parentheses ..
(+10x^2-5x-4x+2)-6=0
We get rid of parentheses
10x^2-5x-4x+2-6=0
We add all the numbers together, and all the variables
10x^2-9x-4=0
a = 10; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·10·(-4)
Δ = 241
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{241}}{2*10}=\frac{9-\sqrt{241}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{241}}{2*10}=\frac{9+\sqrt{241}}{20} $
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