-7/x=-5/4x-3

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

-7/x=-5/4x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-28x)/4x^2+5x/4x^2+3=0

We multiply all the terms by the denominator


(-28x)+5x+3*4x^2=0

We add all the numbers together, and all the variables

5x+(-28x)+3*4x^2=0

Wy multiply elements

12x^2+5x+(-28x)=0

We get rid of parentheses

12x^2+5x-28x=0

We add all the numbers together, and all the variables

12x^2-23x=0

a = 12; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·12·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*12}=\frac{46}{24}
=1+11/12
$