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4x(3x+4)-1=7x
We move all terms to the left:
4x(3x+4)-1-(7x)=0
We add all the numbers together, and all the variables
-7x+4x(3x+4)-1=0
We multiply parentheses
12x^2-7x+16x-1=0
We add all the numbers together, and all the variables
12x^2+9x-1=0
a = 12; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·12·(-1)
Δ = 129
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{-(9)-\sqrt{129}}{2*12}=\frac{-9-\sqrt{129}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*12}=\frac{-9+\sqrt{129}}{24} $
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