-3x-5=6(-1/2x+1)

Solution for -3x-5=6(-1/2x+1) equation:

-3x-5=6(-1/2x+1)

We move all terms to the left:

-3x-5-(6(-1/2x+1))=0


Domain of the equation: 2x+1))!=0

x∈R


We multiply all the terms by the denominator


-3x*2x-5*2x-1+1))-(6(+1))=0

We add all the numbers together, and all the variables

-3x*2x-5*2x-1+1))-(61)=0

We add all the numbers together, and all the variables

-3x*2x-5*2x=0

Wy multiply elements

-6x^2-10x=0

a = -6; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-6)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-6}=\frac{20}{-12}
=-1+2/3
$