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3x(x+4)=4x+1
We move all terms to the left:
3x(x+4)-(4x+1)=0
We multiply parentheses
3x^2+12x-(4x+1)=0
We get rid of parentheses
3x^2+12x-4x-1=0
We add all the numbers together, and all the variables
3x^2+8x-1=0
a = 3; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·3·(-1)
Δ = 76
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*3}=\frac{-8-2\sqrt{19}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*3}=\frac{-8+2\sqrt{19}}{6} $
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