2x-6=-3/4x+5

Solution for 2x-6=-3/4x+5 equation:

2x-6=-3/4x+5

We move all terms to the left:

2x-6-(-3/4x+5)=0


Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

2x+3/4x-5-6=0

We multiply all the terms by the denominator


2x*4x-5*4x-6*4x+3=0

Wy multiply elements

8x^2-20x-24x+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 = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{115}}{2*8}=\frac{44-4\sqrt{115}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{115}}{2*8}=\frac{44+4\sqrt{115}}{16}
$