9/8x=x-14

Solution for 9/8x=x-14 equation:

9/8x=x-14

We move all terms to the left:

9/8x-(x-14)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

9/8x-x+14=0

We multiply all the terms by the denominator


-x*8x+14*8x+9=0

Wy multiply elements

-8x^2+112x+9=0

a = -8; b = 112; c = +9;
Δ = b2-4ac
Δ = 1122-4·(-8)·9
Δ = 12832
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:

$\sqrt{\Delta}=\sqrt{12832}=\sqrt{16*802}=\sqrt{16}*\sqrt{802}=4\sqrt{802}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{802}}{2*-8}=\frac{-112-4\sqrt{802}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{802}}{2*-8}=\frac{-112+4\sqrt{802}}{-16}
$