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6x(4x+2)=x+8
We move all terms to the left:
6x(4x+2)-(x+8)=0
We multiply parentheses
24x^2+12x-(x+8)=0
We get rid of parentheses
24x^2+12x-x-8=0
We add all the numbers together, and all the variables
24x^2+11x-8=0
a = 24; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·24·(-8)
Δ = 889
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{889}}{2*24}=\frac{-11-\sqrt{889}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{889}}{2*24}=\frac{-11+\sqrt{889}}{48} $
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