4x-7/3x=1

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Solution for 4x-7/3x=1 equation: 



4x-7/3x=1

We move all terms to the left:

4x-7/3x-(1)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We multiply all the terms by the denominator


4x*3x-1*3x-7=0

Wy multiply elements

12x^2-3x-7=0

a = 12; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·12·(-7)
Δ = 345
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{-(-3)-\sqrt{345}}{2*12}=\frac{3-\sqrt{345}}{24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{345}}{2*12}=\frac{3+\sqrt{345}}{24}
$

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