2x-1=3/4x-7

Solution for 2x-1=3/4x-7 equation:

2x-1=3/4x-7

We move all terms to the left:

2x-1-(3/4x-7)=0


Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

2x-3/4x+7-1=0

We multiply all the terms by the denominator


2x*4x+7*4x-1*4x-3=0

Wy multiply elements

8x^2+28x-4x-3=0

We add all the numbers together, and all the variables

8x^2+24x-3=0

a = 8; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·8·(-3)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{42}}{2*8}=\frac{-24-4\sqrt{42}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{42}}{2*8}=\frac{-24+4\sqrt{42}}{16}
$