0=(t+0.75)(6-1.5t)

Solution for 0=(t+0.75)(6-1.5t) equation:

0=(t+0.75)(6-1.5t)

We move all terms to the left:

0-((t+0.75)(6-1.5t))=0

We add all the numbers together, and all the variables

-((t+0.75)(-1.5t+6))+0=0

We add all the numbers together, and all the variables

-((t+0.75)(-1.5t+6))=0

We multiply parentheses ..

-((-1t^2+6t-0.75t+4.5))=0


We calculate terms in parentheses: -((-1t^2+6t-0.75t+4.5)), so:

(-1t^2+6t-0.75t+4.5)

We get rid of parentheses

-1t^2+6t-0.75t+4.5

We add all the numbers together, and all the variables

-1t^2+5.25t+4.5

Back to the equation:

-(-1t^2+5.25t+4.5)


We get rid of parentheses

1t^2-5.25t-4.5=0

We add all the numbers together, and all the variables

t^2-5.25t-4.5=0

a = 1; b = -5.25; c = -4.5;
Δ = b2-4ac
Δ = -5.252-4·1·(-4.5)
Δ = 45.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5.25)-\sqrt{45.5625}}{2*1}=\frac{5.25-\sqrt{45.5625}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.25)+\sqrt{45.5625}}{2*1}=\frac{5.25+\sqrt{45.5625}}{2}
$