1/2x-9=7.5+6x

Solution for 1/2x-9=7.5+6x equation:

1/2x-9=7.5+6x

We move all terms to the left:

1/2x-9-(7.5+6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(6x+7.5)-9=0

We get rid of parentheses

1/2x-6x-7.5-9=0

We multiply all the terms by the denominator


-6x*2x-(7.5)*2x-9*2x+1=0

We multiply parentheses

-6x*2x-15x-9*2x+1=0

Wy multiply elements

-12x^2-15x-18x+1=0

We add all the numbers together, and all the variables

-12x^2-33x+1=0

a = -12; b = -33; c = +1;
Δ = b2-4ac
Δ = -332-4·(-12)·1
Δ = 1137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-\sqrt{1137}}{2*-12}=\frac{33-\sqrt{1137}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1137}}{2*-12}=\frac{33+\sqrt{1137}}{-24}
$