0/6x-14=0.5x-6.5

Solution for 0/6x-14=0.5x-6.5 equation:

0/6x-14=0.5x-6.5

We move all terms to the left:

0/6x-14-(0.5x-6.5)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

0/6x-0.5x+6.5-14=0

We multiply all the terms by the denominator


-(0.5x)*6x+(6.5)*6x-14*6x+0=0

We add all the numbers together, and all the variables

-(+0.5x)*6x+(6.5)*6x-14*6x+0=0

We add all the numbers together, and all the variables

-(+0.5x)*6x+(6.5)*6x-14*6x=0

We multiply parentheses

-0x^2+39x-14*6x=0

Wy multiply elements

-0x^2+39x-84x=0

We add all the numbers together, and all the variables

-1x^2-45x=0

a = -1; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·(-1)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*-1}=\frac{90}{-2}
=-45
$