9/8x-x+3=-6

Solution for 9/8x-x+3=-6 equation:

9/8x-x+3=-6

We move all terms to the left:

9/8x-x+3-(-6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+72x+9=0

a = -8; b = 72; c = +9;
Δ = b2-4ac
Δ = 722-4·(-8)·9
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{38}}{2*-8}=\frac{-72-12\sqrt{38}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{38}}{2*-8}=\frac{-72+12\sqrt{38}}{-16}
$