7x+4/x+2=89

Solution for 7x+4/x+2=89 equation:

7x+4/x+2=89

We move all terms to the left:

7x+4/x+2-(89)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x+4/x-87=0

We multiply all the terms by the denominator


7x*x-87*x+4=0

We add all the numbers together, and all the variables

-87x+7x*x+4=0

Wy multiply elements

7x^2-87x+4=0

a = 7; b = -87; c = +4;
Δ = b2-4ac
Δ = -872-4·7·4
Δ = 7457
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{-(-87)-\sqrt{7457}}{2*7}=\frac{87-\sqrt{7457}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+\sqrt{7457}}{2*7}=\frac{87+\sqrt{7457}}{14}
$