8y-3/2y=3

Solution for 8y-3/2y=3 equation:

8y-3/2y=3

We move all terms to the left:

8y-3/2y-(3)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


8y*2y-3*2y-3=0

Wy multiply elements

16y^2-6y-3=0

a = 16; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·16·(-3)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{57}}{2*16}=\frac{6-2\sqrt{57}}{32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{57}}{2*16}=\frac{6+2\sqrt{57}}{32}
$