3/4t-21=0.75t-21

Solution for 3/4t-21=0.75t-21 equation:

3/4t-21=0.75t-21

We move all terms to the left:

3/4t-21-(0.75t-21)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We get rid of parentheses

3/4t-0.75t+21-21=0

We multiply all the terms by the denominator


-(0.75t)*4t+21*4t-21*4t+3=0

We add all the numbers together, and all the variables

-(+0.75t)*4t+21*4t-21*4t+3=0

We multiply parentheses

-0t^2+21*4t-21*4t+3=0

Wy multiply elements

-0t^2+84t-84t+3=0

We add all the numbers together, and all the variables

-1t^2+3=0

a = -1; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-1)·3
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*-1}=\frac{0-2\sqrt{3}}{-2}
=-\frac{2\sqrt{3}}{-2}
=-\frac{\sqrt{3}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*-1}=\frac{0+2\sqrt{3}}{-2}
=\frac{2\sqrt{3}}{-2}
=\frac{\sqrt{3}}{-1}
$