(7t-2)(3t+1)=-3(13t)

Solution for (7t-2)(3t+1)=-3(13t) equation:

(7t-2)(3t+1)=-3(13t)

We move all terms to the left:

(7t-2)(3t+1)-(-3(13t))=0

We get rid of parentheses

(7t-2)(3t+1)+313t=0

We multiply parentheses ..

(+21t^2+7t-6t-2)+313t=0

We get rid of parentheses

21t^2+7t-6t+313t-2=0

We add all the numbers together, and all the variables

21t^2+314t-2=0

a = 21; b = 314; c = -2;
Δ = b2-4ac
Δ = 3142-4·21·(-2)
Δ = 98764
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:

$\sqrt{\Delta}=\sqrt{98764}=\sqrt{4*24691}=\sqrt{4}*\sqrt{24691}=2\sqrt{24691}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(314)-2\sqrt{24691}}{2*21}=\frac{-314-2\sqrt{24691}}{42}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(314)+2\sqrt{24691}}{2*21}=\frac{-314+2\sqrt{24691}}{42}
$