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2(2x+1)1x=x+2x+18
We move all terms to the left:
2(2x+1)1x-(x+2x+18)=0
We add all the numbers together, and all the variables
2(2x+1)1x-(3x+18)=0
We multiply parentheses
4x^2+2x-(3x+18)=0
We get rid of parentheses
4x^2+2x-3x-18=0
We add all the numbers together, and all the variables
4x^2-1x-18=0
a = 4; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·4·(-18)
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*4}=\frac{-16}{8} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*4}=\frac{18}{8} =2+1/4 $
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