-.25x+6=2/3x+28

Solution for -.25x+6=2/3x+28 equation:

-.25x+6=2/3x+28

We move all terms to the left:

-.25x+6-(2/3x+28)=0


Domain of the equation: 3x+28)!=0

x∈R


We add all the numbers together, and all the variables

-0.25x-(2/3x+28)+6=0

We get rid of parentheses

-0.25x-2/3x-28+6=0

We multiply all the terms by the denominator


-(0.25x)*3x-28*3x+6*3x-2=0

We add all the numbers together, and all the variables

-(+0.25x)*3x-28*3x+6*3x-2=0

We multiply parentheses

-0x^2-28*3x+6*3x-2=0

Wy multiply elements

-0x^2-84x+18x-2=0

We add all the numbers together, and all the variables

-1x^2-66x-2=0

a = -1; b = -66; c = -2;
Δ = b2-4ac
Δ = -662-4·(-1)·(-2)
Δ = 4348
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:

$\sqrt{\Delta}=\sqrt{4348}=\sqrt{4*1087}=\sqrt{4}*\sqrt{1087}=2\sqrt{1087}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1087}}{2*-1}=\frac{66-2\sqrt{1087}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1087}}{2*-1}=\frac{66+2\sqrt{1087}}{-2}
$