4/x-5=7x

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

4/x-5=7x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-7x+4/x-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-7x^2-5x+4=0

a = -7; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-7)·4
Δ = 137
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{-(-5)-\sqrt{137}}{2*-7}=\frac{5-\sqrt{137}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{137}}{2*-7}=\frac{5+\sqrt{137}}{-14}
$