y+10-3/y=7

Solution for y+10-3/y=7 equation:

y+10-3/y=7

We move all terms to the left:

y+10-3/y-(7)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y-3/y+3=0

We multiply all the terms by the denominator


y*y+3*y-3=0

We add all the numbers together, and all the variables

3y+y*y-3=0

Wy multiply elements

y^2+3y-3=0

a = 1; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·1·(-3)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{21}}{2*1}=\frac{-3-\sqrt{21}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*1}=\frac{-3+\sqrt{21}}{2}
$