3/4x+3=8x-8

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

3/4x+3=8x-8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-32x^2+32x+12x+3=0

We add all the numbers together, and all the variables

-32x^2+44x+3=0

a = -32; b = 44; c = +3;
Δ = b2-4ac
Δ = 442-4·(-32)·3
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{145}}{2*-32}=\frac{-44-4\sqrt{145}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{145}}{2*-32}=\frac{-44+4\sqrt{145}}{-64}
$