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4x(x-1)+2x(x+1)=5
We move all terms to the left:
4x(x-1)+2x(x+1)-(5)=0
We multiply parentheses
4x^2+2x^2-4x+2x-5=0
We add all the numbers together, and all the variables
6x^2-2x-5=0
a = 6; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·6·(-5)
Δ = 124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*6}=\frac{2-2\sqrt{31}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*6}=\frac{2+2\sqrt{31}}{12} $
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