T2x-2=3(x/1)-5(6-2x)

Solution for T2x-2=3(x/1)-5(6-2x) equation:

2T-2=3(T/1)-5(6-2T)

We move all terms to the left:

2T-2-(3(T/1)-5(6-2T))=0


Domain of the equation: 1)-5(6-2T))!=0

T∈R


We add all the numbers together, and all the variables

2T-(3(+T/1)-5(-2T+6))-2=0

We multiply all the terms by the denominator


2T*1)-5(-2T+T-2T+6))-(3(-2*1)-5(+6))=0

We add all the numbers together, and all the variables

2T*1)-5(-3T+6))-(3(-2)-56)=0

We add all the numbers together, and all the variables

-3T+2T*1)-5(=0

Wy multiply elements

2T^2-3T=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*2}=\frac{0}{4}
=0
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$