t+5/t-5=10

Solution for t+5/t-5=10 equation:

t+5/t-5=10

We move all terms to the left:

t+5/t-5-(10)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

t+5/t-15=0

We multiply all the terms by the denominator


t*t-15*t+5=0

We add all the numbers together, and all the variables

-15t+t*t+5=0

Wy multiply elements

t^2-15t+5=0

a = 1; b = -15; c = +5;
Δ = b2-4ac
Δ = -152-4·1·5
Δ = 205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{205}}{2*1}=\frac{15-\sqrt{205}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{205}}{2*1}=\frac{15+\sqrt{205}}{2}
$