10t^2=7t+1

Solution for 10t^2=7t+1 equation:

10t^2=7t+1

We move all terms to the left:

10t^2-(7t+1)=0

We get rid of parentheses

10t^2-7t-1=0

a = 10; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·10·(-1)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{89}}{2*10}=\frac{7-\sqrt{89}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*10}=\frac{7+\sqrt{89}}{20}
$