-7(x)=-29/x-4

Solution for -7(x)=-29/x-4 equation:

-7(x)=-29/x-4

We move all terms to the left:

-7(x)-(-29/x-4)=0


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

x∈R


We get rid of parentheses

-7x+29/x+4=0

We multiply all the terms by the denominator


-7x*x+4*x+29=0

We add all the numbers together, and all the variables

4x-7x*x+29=0

Wy multiply elements

-7x^2+4x+29=0

a = -7; b = 4; c = +29;
Δ = b2-4ac
Δ = 42-4·(-7)·29
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{23}}{2*-7}=\frac{-4-6\sqrt{23}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{23}}{2*-7}=\frac{-4+6\sqrt{23}}{-14}
$