4x-8/x-3=4

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

4x-8/x-3=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-8/x-7=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-7x-8=0

a = 4; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·4·(-8)
Δ = 177
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{-(-7)-\sqrt{177}}{2*4}=\frac{7-\sqrt{177}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*4}=\frac{7+\sqrt{177}}{8}
$