((7/2)t)-2=4+7t

Solution for ((7/2)t)-2=4+7t equation:

((7/2)t)-2=4+7t

We move all terms to the left:

((7/2)t)-2-(4+7t)=0


Domain of the equation: 2)t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

((+7/2)t)-(7t+4)-2=0

We get rid of parentheses

((+7/2)t)-7t-4-2=0

We multiply all the terms by the denominator


((+7-7t*2)t)-4*2)t)-2*2)t)=0


We calculate terms in parentheses: +((+7-7t*2)t), so:

(+7-7t*2)t

We add all the numbers together, and all the variables

(-7t*2+7)t

We multiply parentheses

-14t^2+7t

Back to the equation:

+(-14t^2+7t)


Wy multiply elements

(-14t^2+7t)-16t^2=0

We get rid of parentheses

-14t^2-16t^2+7t=0

We add all the numbers together, and all the variables

-30t^2+7t=0

a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60}
=7/30
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60}
=0
$