X-12=-3/4y

Solution for X-12=-3/4y equation:

X-12=-3/4X

We move all terms to the left:

X-12-(-3/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We get rid of parentheses

X+3/4X-12=0

We multiply all the terms by the denominator


X*4X-12*4X+3=0

Wy multiply elements

4X^2-48X+3=0

a = 4; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·4·3
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{141}}{2*4}=\frac{48-4\sqrt{141}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{141}}{2*4}=\frac{48+4\sqrt{141}}{8}
$