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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-32x-12x+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}
$