x=7/8x+6

Solution for x=7/8x+6 equation:

x=7/8x+6

We move all terms to the left:

x-(7/8x+6)=0


Domain of the equation: 8x+6)!=0

x∈R


We get rid of parentheses

x-7/8x-6=0

We multiply all the terms by the denominator


x*8x-6*8x-7=0

Wy multiply elements

8x^2-48x-7=0

a = 8; b = -48; c = -7;
Δ = b2-4ac
Δ = -482-4·8·(-7)
Δ = 2528
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:

$\sqrt{\Delta}=\sqrt{2528}=\sqrt{16*158}=\sqrt{16}*\sqrt{158}=4\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{158}}{2*8}=\frac{48-4\sqrt{158}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{158}}{2*8}=\frac{48+4\sqrt{158}}{16}
$