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^2-64X-7=0

a = 8; b = -64; c = -7;
Δ = b2-4ac
Δ = -642-4·8·(-7)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-12\sqrt{30}}{2*8}=\frac{64-12\sqrt{30}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+12\sqrt{30}}{2*8}=\frac{64+12\sqrt{30}}{16}
$