7t(t-2)=2t-9

Solution for 7t(t-2)=2t-9 equation:

7t(t-2)=2t-9

We move all terms to the left:

7t(t-2)-(2t-9)=0

We multiply parentheses

7t^2-14t-(2t-9)=0

We get rid of parentheses

7t^2-14t-2t+9=0

We add all the numbers together, and all the variables

7t^2-16t+9=0

a = 7; b = -16; c = +9;
Δ = b2-4ac
Δ = -162-4·7·9
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2}{2*7}=\frac{14}{14}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2}{2*7}=\frac{18}{14}
=1+2/7
$