6t-4/3t-2=-7)2

Solution for 6t-4/3t-2=-7)2 equation:

6t-4/3t-2=-7)2

We move all terms to the left:

6t-4/3t-2-(-7)2)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

6t-4/3t=0

We multiply all the terms by the denominator


6t*3t-4=0

Wy multiply elements

18t^2-4=0

a = 18; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·18·(-4)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*18}=\frac{0-12\sqrt{2}}{36}
=-\frac{12\sqrt{2}}{36}
=-\frac{\sqrt{2}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*18}=\frac{0+12\sqrt{2}}{36}
=\frac{12\sqrt{2}}{36}
=\frac{\sqrt{2}}{3}
$