175=7x+8/x+4

Solution for 175=7x+8/x+4 equation:

175=7x+8/x+4

We move all terms to the left:

175-(7x+8/x+4)=0


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

x∈R


We get rid of parentheses

-7x-8/x-4+175=0

We multiply all the terms by the denominator


-7x*x-4*x+175*x-8=0

We add all the numbers together, and all the variables

171x-7x*x-8=0

Wy multiply elements

-7x^2+171x-8=0

a = -7; b = 171; c = -8;
Δ = b2-4ac
Δ = 1712-4·(-7)·(-8)
Δ = 29017
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{-(171)-\sqrt{29017}}{2*-7}=\frac{-171-\sqrt{29017}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+\sqrt{29017}}{2*-7}=\frac{-171+\sqrt{29017}}{-14}
$