-.5(t+9)+5.75t=3/8t

Solution for -.5(t+9)+5.75t=3/8t equation:

-.5(t+9)+5.75t=3/8t

We move all terms to the left:

-.5(t+9)+5.75t-(3/8t)=0


Domain of the equation: 8t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-.5(t+9)+5.75t-(+3/8t)=0

We add all the numbers together, and all the variables

5.75t-.5(t+9)-(+3/8t)=0

We multiply parentheses

5.75t-0.5t-(+3/8t)-4.5=0

We get rid of parentheses

5.75t-0.5t-3/8t-4.5=0

We multiply all the terms by the denominator


(5.75t)*8t-(0.5t)*8t-(4.5)*8t-3=0

We add all the numbers together, and all the variables

(+5.75t)*8t-(+0.5t)*8t-(4.5)*8t-3=0

We multiply parentheses

40t^2-0t^2-36t-3=0

We add all the numbers together, and all the variables

39t^2-36t-3=0

a = 39; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·39·(-3)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-42}{2*39}=\frac{-6}{78}
=-1/13
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+42}{2*39}=\frac{78}{78}
=1
$