.25x+1/3x+8=22

Solution for .25x+1/3x+8=22 equation:

.25x+1/3x+8=22

We move all terms to the left:

.25x+1/3x+8-(22)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

.25x+1/3x-14=0

We multiply all the terms by the denominator


(.25x)*3x-14*3x+1=0

We add all the numbers together, and all the variables

(+.25x)*3x-14*3x+1=0

We multiply parentheses

3x^2-14*3x+1=0

Wy multiply elements

3x^2-42x+1=0

a = 3; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·3·1
Δ = 1752
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:

$\sqrt{\Delta}=\sqrt{1752}=\sqrt{4*438}=\sqrt{4}*\sqrt{438}=2\sqrt{438}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{438}}{2*3}=\frac{42-2\sqrt{438}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{438}}{2*3}=\frac{42+2\sqrt{438}}{6}
$