x=3/4x-8

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

x=3/4x-8

We move all terms to the left:

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


Domain of the equation: 4x-8)!=0

x∈R


We get rid of parentheses

x-3/4x+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+32x-3=0

a = 4; b = 32; c = -3;
Δ = b2-4ac
Δ = 322-4·4·(-3)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{67}}{2*4}=\frac{-32-4\sqrt{67}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{67}}{2*4}=\frac{-32+4\sqrt{67}}{8}
$