6t=7(t-1/2)

Solution for 6t=7(t-1/2) equation:

6t=7(t-1/2)

We move all terms to the left:

6t-(7(t-1/2))=0

We add all the numbers together, and all the variables

6t-(7(+t-1/2))=0

We multiply all the terms by the denominator


6t*2))-(7(+t-1=0

We add all the numbers together, and all the variables

t+6t*2))-(7(-1=0

Wy multiply elements

12t^2+t-1=0

a = 12; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·12·(-1)
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{-(1)-7}{2*12}=\frac{-8}{24}
=-1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*12}=\frac{6}{24}
=1/4
$