X=3/4y+3

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

X=3/4X+3

We move all terms to the left:

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


Domain of the equation: 4X+3)!=0

X∈R


We get rid of parentheses

X-3/4X-3=0

We multiply all the terms by the denominator


X*4X-3*4X-3=0

Wy multiply elements

4X^2-12X-3=0

a = 4; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·4·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*4}=\frac{12-8\sqrt{3}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*4}=\frac{12+8\sqrt{3}}{8}
$