6.75x+3/8x=13.25

Solution for 6.75x+3/8x=13.25 equation:

6.75x+3/8x=13.25

We move all terms to the left:

6.75x+3/8x-(13.25)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

6.75x+3/8x-13.25=0

We multiply all the terms by the denominator


(6.75x)*8x-(13.25)*8x+3=0

We add all the numbers together, and all the variables

(+6.75x)*8x-(13.25)*8x+3=0

We multiply parentheses

48x^2-106x+3=0

a = 48; b = -106; c = +3;
Δ = b2-4ac
Δ = -1062-4·48·3
Δ = 10660
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:

$\sqrt{\Delta}=\sqrt{10660}=\sqrt{4*2665}=\sqrt{4}*\sqrt{2665}=2\sqrt{2665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{2665}}{2*48}=\frac{106-2\sqrt{2665}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{2665}}{2*48}=\frac{106+2\sqrt{2665}}{96}
$