x-9=7/8x+1

Solution for x-9=7/8x+1 equation:

x-9=7/8x+1

We move all terms to the left:

x-9-(7/8x+1)=0


Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

x-7/8x-1-9=0

We multiply all the terms by the denominator


x*8x-1*8x-9*8x-7=0

Wy multiply elements

8x^2-8x-72x-7=0

We add all the numbers together, and all the variables

8x^2-80x-7=0

a = 8; b = -80; c = -7;
Δ = b2-4ac
Δ = -802-4·8·(-7)
Δ = 6624
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:

$\sqrt{\Delta}=\sqrt{6624}=\sqrt{144*46}=\sqrt{144}*\sqrt{46}=12\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-12\sqrt{46}}{2*8}=\frac{80-12\sqrt{46}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+12\sqrt{46}}{2*8}=\frac{80+12\sqrt{46}}{16}
$