7x-5/3x=4

Solution for 7x-5/3x=4 equation:

7x-5/3x=4

We move all terms to the left:

7x-5/3x-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


7x*3x-4*3x-5=0

Wy multiply elements

21x^2-12x-5=0

a = 21; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·21·(-5)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{141}}{2*21}=\frac{12-2\sqrt{141}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{141}}{2*21}=\frac{12+2\sqrt{141}}{42}
$