5t^2=8-3t

Solution for 5t^2=8-3t equation:

5t^2=8-3t

We move all terms to the left:

5t^2-(8-3t)=0

We add all the numbers together, and all the variables

5t^2-(-3t+8)=0

We get rid of parentheses

5t^2+3t-8=0

a = 5; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·5·(-8)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*5}=\frac{-16}{10}
=-1+3/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*5}=\frac{10}{10}
=1
$