0.75x+2-1/3x=12

Solution for 0.75x+2-1/3x=12 equation:

0.75x+2-1/3x=12

We move all terms to the left:

0.75x+2-1/3x-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

0.75x-1/3x-10=0

We multiply all the terms by the denominator


(0.75x)*3x-10*3x-1=0

We add all the numbers together, and all the variables

(+0.75x)*3x-10*3x-1=0

We multiply parentheses

0x^2-10*3x-1=0

Wy multiply elements

0x^2-30x-1=0

We add all the numbers together, and all the variables

x^2-30x-1=0

a = 1; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·1·(-1)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{226}}{2*1}=\frac{30-2\sqrt{226}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{226}}{2*1}=\frac{30+2\sqrt{226}}{2}
$