5=7t^2/6

Solution for 5=7t^2/6 equation:

5=7t^2/6

We move all terms to the left:

5-(7t^2/6)=0

We get rid of parentheses

-7t^2/6+5=0

We multiply all the terms by the denominator


-7t^2+5*6=0

We add all the numbers together, and all the variables

-7t^2+30=0

a = -7; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-7)·30
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*-7}=\frac{0-2\sqrt{210}}{-14}
=-\frac{2\sqrt{210}}{-14}
=-\frac{\sqrt{210}}{-7}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*-7}=\frac{0+2\sqrt{210}}{-14}
=\frac{2\sqrt{210}}{-14}
=\frac{\sqrt{210}}{-7}
$