3/4X+3,X=4,y=3

Solution for 3/4X+3,X=4,y=3 equation:

3/4X+3.X=4.X=3

We move all terms to the left:

3/4X+3.X-(4.X)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

3/4X+3.X-(+4.X)=0

We add all the numbers together, and all the variables

3.X+3/4X-(+4.X)=0

We get rid of parentheses

3.X+3/4X-4.X=0

We multiply all the terms by the denominator


(3.X)*4X-(4.X)*4X+3=0

We add all the numbers together, and all the variables

(+3.X)*4X-(+4.X)*4X+3=0

We multiply parentheses

12X^2-16X^2+3=0

We add all the numbers together, and all the variables

-4X^2+3=0

a = -4; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-4)·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-4}=\frac{0-4\sqrt{3}}{-8}
=-\frac{4\sqrt{3}}{-8}
=-\frac{\sqrt{3}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-4}=\frac{0+4\sqrt{3}}{-8}
=\frac{4\sqrt{3}}{-8}
=\frac{\sqrt{3}}{-2}
$