7t-7=2(1/2t-3)+6

Solution for 7t-7=2(1/2t-3)+6 equation:

7t-7=2(1/2t-3)+6

We move all terms to the left:

7t-7-(2(1/2t-3)+6)=0


Domain of the equation: 2t-3)+6)!=0

t∈R


We multiply all the terms by the denominator


7t*2t-7*2t-3)+6)-(2(1-3)+6)=0

We add all the numbers together, and all the variables

7t*2t-7*2t-3)+6)-(2(-2)+6)=0

We add all the numbers together, and all the variables

7t*2t-7*2t=0

Wy multiply elements

14t^2-14t=0

a = 14; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·14·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*14}=\frac{0}{28}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*14}=\frac{28}{28}
=1
$