2x-3/4x-4x+8=0

Solution for 2x-3/4x-4x+8=0 equation:

2x-3/4x-4x+8=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-2x-3/4x+8=0

We multiply all the terms by the denominator


-2x*4x+8*4x-3=0

Wy multiply elements

-8x^2+32x-3=0

a = -8; b = 32; c = -3;
Δ = b2-4ac
Δ = 322-4·(-8)·(-3)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{58}}{2*-8}=\frac{-32-4\sqrt{58}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{58}}{2*-8}=\frac{-32+4\sqrt{58}}{-16}
$