7x-4/4x=2

Solution for 7x-4/4x=2 equation:

7x-4/4x=2

We move all terms to the left:

7x-4/4x-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


7x*4x-2*4x-4=0

Wy multiply elements

28x^2-8x-4=0

a = 28; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·28·(-4)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{2}}{2*28}=\frac{8-16\sqrt{2}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{2}}{2*28}=\frac{8+16\sqrt{2}}{56}
$