5x-7/3x=-4

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

5x-7/3x=-4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x-7/3x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2+12x-7=0

a = 15; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·15·(-7)
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*15}=\frac{-12-2\sqrt{141}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{141}}{2*15}=\frac{-12+2\sqrt{141}}{30}
$