7y-12/2y=5

Solution for 7y-12/2y=5 equation:

7y-12/2y=5

We move all terms to the left:

7y-12/2y-(5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


7y*2y-5*2y-12=0

Wy multiply elements

14y^2-10y-12=0

a = 14; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·14·(-12)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{193}}{2*14}=\frac{10-2\sqrt{193}}{28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{193}}{2*14}=\frac{10+2\sqrt{193}}{28}
$