2x-2=3/4x-13

Solution for 2x-2=3/4x-13 equation:

2x-2=3/4x-13

We move all terms to the left:

2x-2-(3/4x-13)=0


Domain of the equation: 4x-13)!=0

x∈R


We get rid of parentheses

2x-3/4x+13-2=0

We multiply all the terms by the denominator


2x*4x+13*4x-2*4x-3=0

Wy multiply elements

8x^2+52x-8x-3=0

We add all the numbers together, and all the variables

8x^2+44x-3=0

a = 8; b = 44; c = -3;
Δ = b2-4ac
Δ = 442-4·8·(-3)
Δ = 2032
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:

$\sqrt{\Delta}=\sqrt{2032}=\sqrt{16*127}=\sqrt{16}*\sqrt{127}=4\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{127}}{2*8}=\frac{-44-4\sqrt{127}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{127}}{2*8}=\frac{-44+4\sqrt{127}}{16}
$