18t^2-10.5t-19=1-1.5t

Solution for 18t^2-10.5t-19=1-1.5t equation:

18t^2-10.5t-19=1-1.5t

We move all terms to the left:

18t^2-10.5t-19-(1-1.5t)=0

We add all the numbers together, and all the variables

18t^2-10.5t-(-1.5t+1)-19=0

We get rid of parentheses

18t^2-10.5t+1.5t-1-19=0

We add all the numbers together, and all the variables

18t^2-9t-20=0

a = 18; b = -9; c = -20;
Δ = b2-4ac
Δ = -92-4·18·(-20)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*18}=\frac{-30}{36}
=-5/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*18}=\frac{48}{36}
=1+1/3
$