5/7t=5t=

Solution for 5/7t=5t= equation:

5/7t=5t=

We move all terms to the left:

5/7t-(5t)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R


We add all the numbers together, and all the variables

-5t+5/7t=0

We multiply all the terms by the denominator


-5t*7t+5=0

Wy multiply elements

-35t^2+5=0

a = -35; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-35)·5
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*-35}=\frac{0-10\sqrt{7}}{-70}
=-\frac{10\sqrt{7}}{-70}
=-\frac{\sqrt{7}}{-7}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*-35}=\frac{0+10\sqrt{7}}{-70}
=\frac{10\sqrt{7}}{-70}
=\frac{\sqrt{7}}{-7}
$