7t^2+2t=5

Solution for 7t^2+2t=5 equation:

7t^2+2t=5

We move all terms to the left:

7t^2+2t-(5)=0

a = 7; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·7·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*7}=\frac{-14}{14}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*7}=\frac{10}{14}
=5/7
$