15y-20/2y=7

Solution for 15y-20/2y=7 equation:

15y-20/2y=7

We move all terms to the left:

15y-20/2y-(7)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


15y*2y-7*2y-20=0

Wy multiply elements

30y^2-14y-20=0

a = 30; b = -14; c = -20;
Δ = b2-4ac
Δ = -142-4·30·(-20)
Δ = 2596
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:

$\sqrt{\Delta}=\sqrt{2596}=\sqrt{4*649}=\sqrt{4}*\sqrt{649}=2\sqrt{649}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{649}}{2*30}=\frac{14-2\sqrt{649}}{60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{649}}{2*30}=\frac{14+2\sqrt{649}}{60}
$