t*t=2+6/7

Solution for t*t=2+6/7 equation:

t*t=2+6/7

We move all terms to the left:

t*t-(2+6/7)=0

We add all the numbers together, and all the variables

t*t-(6/7+2)=0

Wy multiply elements

t^2-(6/7+2)=0

We get rid of parentheses

t^2-2-6/7=0

We multiply all the terms by the denominator


t^2*7-6-2*7=0

We add all the numbers together, and all the variables

t^2*7-20=0

Wy multiply elements

7t^2-20=0

a = 7; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·7·(-20)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*7}=\frac{0-4\sqrt{35}}{14}
=-\frac{4\sqrt{35}}{14}
=-\frac{2\sqrt{35}}{7}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*7}=\frac{0+4\sqrt{35}}{14}
=\frac{4\sqrt{35}}{14}
=\frac{2\sqrt{35}}{7}
$