15t^2+10t+20=5t^2+40t

Solution for 15t^2+10t+20=5t^2+40t equation:

15t^2+10t+20=5t^2+40t

We move all terms to the left:

15t^2+10t+20-(5t^2+40t)=0

We get rid of parentheses

15t^2-5t^2+10t-40t+20=0

We add all the numbers together, and all the variables

10t^2-30t+20=0

a = 10; b = -30; c = +20;
Δ = b2-4ac
Δ = -302-4·10·20
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*10}=\frac{20}{20}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*10}=\frac{40}{20}
=2
$