X+3/x+7x/x+3=23/4

Solution for X+3/x+7x/x+3=23/4 equation:

X+3/X+7X/X+3=23/4

We move all terms to the left:

X+3/X+7X/X+3-(23/4)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+3/X+7X/X+3-(+23/4)=0

We get rid of parentheses

X+3/X+7X/X+3-23/4=0

We calculate fractions


X+(28X+3)/4X+(-23X)/4X+3=0

We multiply all the terms by the denominator


X*4X+(28X+3)+(-23X)+3*4X=0

Wy multiply elements

4X^2+(28X+3)+(-23X)+12X=0

We get rid of parentheses

4X^2+28X-23X+12X+3=0

We add all the numbers together, and all the variables

4X^2+17X+3=0

a = 4; b = 17; c = +3;
Δ = b2-4ac
Δ = 172-4·4·3
Δ = 241
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{-(17)-\sqrt{241}}{2*4}=\frac{-17-\sqrt{241}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{241}}{2*4}=\frac{-17+\sqrt{241}}{8}
$