y=3/4y-6

Solution for y=3/4y-6 equation:

y=3/4y-6

We move all terms to the left:

y-(3/4y-6)=0


Domain of the equation: 4y-6)!=0

y∈R


We get rid of parentheses

y-3/4y+6=0

We multiply all the terms by the denominator


y*4y+6*4y-3=0

Wy multiply elements

4y^2+24y-3=0

a = 4; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·4·(-3)
Δ = 624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*4}=\frac{-24-4\sqrt{39}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*4}=\frac{-24+4\sqrt{39}}{8}
$