y+3/4(y)=21

Solution for y+3/4(y)=21 equation:

y+3/4(y)=21

We move all terms to the left:

y+3/4(y)-(21)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We multiply all the terms by the denominator


y*4y-21*4y+3=0

Wy multiply elements

4y^2-84y+3=0

a = 4; b = -84; c = +3;
Δ = b2-4ac
Δ = -842-4·4·3
Δ = 7008
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:

$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{438}}{2*4}=\frac{84-4\sqrt{438}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{438}}{2*4}=\frac{84+4\sqrt{438}}{8}
$