-.25x+6=2/3x+2

Solution for -.25x+6=2/3x+2 equation:

-.25x+6=2/3x+2

We move all terms to the left:

-.25x+6-(2/3x+2)=0


Domain of the equation: 3x+2)!=0

x∈R


We add all the numbers together, and all the variables

-0.25x-(2/3x+2)+6=0

We get rid of parentheses

-0.25x-2/3x-2+6=0

We multiply all the terms by the denominator


-(0.25x)*3x-2*3x+6*3x-2=0

We add all the numbers together, and all the variables

-(+0.25x)*3x-2*3x+6*3x-2=0

We multiply parentheses

-0x^2-2*3x+6*3x-2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -1; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·(-1)·(-2)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{34}}{2*-1}=\frac{-12-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{34}}{2*-1}=\frac{-12+2\sqrt{34}}{-2}
$