x-7/4x-7=25

Solution for x-7/4x-7=25 equation:

x-7/4x-7=25

We move all terms to the left:

x-7/4x-7-(25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x-7/4x-32=0

We multiply all the terms by the denominator


x*4x-32*4x-7=0

Wy multiply elements

4x^2-128x-7=0

a = 4; b = -128; c = -7;
Δ = b2-4ac
Δ = -1282-4·4·(-7)
Δ = 16496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16496}=\sqrt{16*1031}=\sqrt{16}*\sqrt{1031}=4\sqrt{1031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-4\sqrt{1031}}{2*4}=\frac{128-4\sqrt{1031}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+4\sqrt{1031}}{2*4}=\frac{128+4\sqrt{1031}}{8}
$