4y-7/2y=9

Solution for 4y-7/2y=9 equation:

4y-7/2y=9

We move all terms to the left:

4y-7/2y-(9)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


4y*2y-9*2y-7=0

Wy multiply elements

8y^2-18y-7=0

a = 8; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·8·(-7)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{137}}{2*8}=\frac{18-2\sqrt{137}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{137}}{2*8}=\frac{18+2\sqrt{137}}{16}
$