5t=11/7t+15

Solution for 5t=11/7t+15 equation:

5t=11/7t+15

We move all terms to the left:

5t-(11/7t+15)=0


Domain of the equation: 7t+15)!=0

t∈R


We get rid of parentheses

5t-11/7t-15=0

We multiply all the terms by the denominator


5t*7t-15*7t-11=0

Wy multiply elements

35t^2-105t-11=0

a = 35; b = -105; c = -11;
Δ = b2-4ac
Δ = -1052-4·35·(-11)
Δ = 12565
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{-(-105)-\sqrt{12565}}{2*35}=\frac{105-\sqrt{12565}}{70}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{12565}}{2*35}=\frac{105+\sqrt{12565}}{70}
$