8x+7/x+7=22

Solution for 8x+7/x+7=22 equation:

8x+7/x+7=22

We move all terms to the left:

8x+7/x+7-(22)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

8x+7/x-15=0

We multiply all the terms by the denominator


8x*x-15*x+7=0

We add all the numbers together, and all the variables

-15x+8x*x+7=0

Wy multiply elements

8x^2-15x+7=0

a = 8; b = -15; c = +7;
Δ = b2-4ac
Δ = -152-4·8·7
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*8}=\frac{14}{16}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*8}=\frac{16}{16}
=1
$