4/x-2=9-7x

Solution for 4/x-2=9-7x equation:

4/x-2=9-7x

We move all terms to the left:

4/x-2-(9-7x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(-7x+9)-2=0

We get rid of parentheses

4/x+7x-9-2=0

We multiply all the terms by the denominator


7x*x-9*x-2*x+4=0

We add all the numbers together, and all the variables

-11x+7x*x+4=0

Wy multiply elements

7x^2-11x+4=0

a = 7; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·7·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*7}=\frac{8}{14}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*7}=\frac{14}{14}
=1
$