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6x(x+1)-2x(x+2)=9x-2
We move all terms to the left:
6x(x+1)-2x(x+2)-(9x-2)=0
We multiply parentheses
6x^2-2x^2+6x-4x-(9x-2)=0
We get rid of parentheses
6x^2-2x^2+6x-4x-9x+2=0
We add all the numbers together, and all the variables
4x^2-7x+2=0
a = 4; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·4·2
Δ = 17
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{-(-7)-\sqrt{17}}{2*4}=\frac{7-\sqrt{17}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{17}}{2*4}=\frac{7+\sqrt{17}}{8} $
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