1/2x+9-3x=67

Solution for 1/2x+9-3x=67 equation:

1/2x+9-3x=67

We move all terms to the left:

1/2x+9-3x-(67)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/2x-58=0

We multiply all the terms by the denominator


-3x*2x-58*2x+1=0

Wy multiply elements

-6x^2-116x+1=0

a = -6; b = -116; c = +1;
Δ = b2-4ac
Δ = -1162-4·(-6)·1
Δ = 13480
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:

$\sqrt{\Delta}=\sqrt{13480}=\sqrt{4*3370}=\sqrt{4}*\sqrt{3370}=2\sqrt{3370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-2\sqrt{3370}}{2*-6}=\frac{116-2\sqrt{3370}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+2\sqrt{3370}}{2*-6}=\frac{116+2\sqrt{3370}}{-12}
$