1/2x-3(1/2x+5)=-1/2x+9

Solution for 1/2x-3(1/2x+5)=-1/2x+9 equation:

1/2x-3(1/2x+5)=-1/2x+9

We move all terms to the left:

1/2x-3(1/2x+5)-(-1/2x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We multiply parentheses

1/2x-3x-(-1/2x+9)-15=0

We get rid of parentheses

1/2x-3x+1/2x-9-15=0

We multiply all the terms by the denominator


-3x*2x-9*2x-15*2x+1+1=0

We add all the numbers together, and all the variables

-3x*2x-9*2x-15*2x+2=0

Wy multiply elements

-6x^2-18x-30x+2=0

We add all the numbers together, and all the variables

-6x^2-48x+2=0

a = -6; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·(-6)·2
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*-6}=\frac{48-28\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*-6}=\frac{48+28\sqrt{3}}{-12}
$