65/17t=4t

Solution for 65/17t=4t equation:

65/17t=4t

We move all terms to the left:

65/17t-(4t)=0


Domain of the equation: 17t!=0

t!=0/17

t!=0

t∈R


We add all the numbers together, and all the variables

-4t+65/17t=0

We multiply all the terms by the denominator


-4t*17t+65=0

Wy multiply elements

-68t^2+65=0

a = -68; b = 0; c = +65;
Δ = b2-4ac
Δ = 02-4·(-68)·65
Δ = 17680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17680}=\sqrt{16*1105}=\sqrt{16}*\sqrt{1105}=4\sqrt{1105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1105}}{2*-68}=\frac{0-4\sqrt{1105}}{-136}
=-\frac{4\sqrt{1105}}{-136}
=-\frac{\sqrt{1105}}{-34}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1105}}{2*-68}=\frac{0+4\sqrt{1105}}{-136}
=\frac{4\sqrt{1105}}{-136}
=\frac{\sqrt{1105}}{-34}
$