x=3/4(x)+8

Solution for x=3/4(x)+8 equation:

x=3/4(x)+8

We move all terms to the left:

x-(3/4(x)+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}
$