22=7x-6/x+4

Solution for 22=7x-6/x+4 equation:

22=7x-6/x+4

We move all terms to the left:

22-(7x-6/x+4)=0


Domain of the equation: x+4)!=0

x∈R


We get rid of parentheses

-7x+6/x-4+22=0

We multiply all the terms by the denominator


-7x*x-4*x+22*x+6=0

We add all the numbers together, and all the variables

18x-7x*x+6=0

Wy multiply elements

-7x^2+18x+6=0

a = -7; b = 18; c = +6;
Δ = b2-4ac
Δ = 182-4·(-7)·6
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{123}}{2*-7}=\frac{-18-2\sqrt{123}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{123}}{2*-7}=\frac{-18+2\sqrt{123}}{-14}
$