4+3x/x-8=7/8-x

Solution for 4+3x/x-8=7/8-x equation:

4+3x/x-8=7/8-x

We move all terms to the left:

4+3x/x-8-(7/8-x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-8

x!=-8/1

x!=-8

x∈R


We add all the numbers together, and all the variables

3x/x-(-1x+7/8)+4-8=0

We add all the numbers together, and all the variables

3x/x-(-1x+7/8)-4=0

We get rid of parentheses

3x/x+1x-4-7/8=0

We calculate fractions


1x+24x/8x+(-7x)/8x-4=0

We add all the numbers together, and all the variables

x+24x/8x+(-7x)/8x-4=0

We multiply all the terms by the denominator


x*8x+24x+(-7x)-4*8x=0

We add all the numbers together, and all the variables

24x+x*8x+(-7x)-4*8x=0

Wy multiply elements

8x^2+24x+(-7x)-32x=0

We get rid of parentheses

8x^2+24x-7x-32x=0

We add all the numbers together, and all the variables

8x^2-15x=0

a = 8; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·8·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*8}=\frac{30}{16}
=1+7/8
$