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6x(4x+1)+(4x+1)=0
We multiply parentheses
24x^2+6x+(4x+1)=0
We get rid of parentheses
24x^2+6x+4x+1=0
We add all the numbers together, and all the variables
24x^2+10x+1=0
a = 24; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·24·1
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*24}=\frac{-12}{48} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*24}=\frac{-8}{48} =-1/6 $
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