(13t+8)(5t-15)=0

Solution for (13t+8)(5t-15)=0 equation:

(13t+8)(5t-15)=0

We multiply parentheses ..

(+65t^2-195t+40t-120)=0

We get rid of parentheses

65t^2-195t+40t-120=0

We add all the numbers together, and all the variables

65t^2-155t-120=0

a = 65; b = -155; c = -120;
Δ = b2-4ac
Δ = -1552-4·65·(-120)
Δ = 55225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55225}=235$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-155)-235}{2*65}=\frac{-80}{130}
=-8/13
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+235}{2*65}=\frac{390}{130}
=3
$