3t-12t(3+t)-4t=-(5-t)-(7-t)

Solution for 3t-12t(3+t)-4t=-(5-t)-(7-t) equation:

3t-12t(3+t)-4t=-(5-t)-(7-t)

We move all terms to the left:

3t-12t(3+t)-4t-(-(5-t)-(7-t))=0

We add all the numbers together, and all the variables

3t-12t(t+3)-4t-(-(-1t+5)-(-1t+7))=0

We add all the numbers together, and all the variables

-1t-12t(t+3)-(-(-1t+5)-(-1t+7))=0

We multiply parentheses

-12t^2-1t-36t-(-(-1t+5)-(-1t+7))=0


We calculate terms in parentheses: -(-(-1t+5)-(-1t+7)), so:

-(-1t+5)-(-1t+7)

We get rid of parentheses

1t+1t-5-7

We add all the numbers together, and all the variables

2t-12

Back to the equation:

-(2t-12)


We add all the numbers together, and all the variables

-12t^2-37t-(2t-12)=0

We get rid of parentheses

-12t^2-37t-2t+12=0

We add all the numbers together, and all the variables

-12t^2-39t+12=0

a = -12; b = -39; c = +12;
Δ = b2-4ac
Δ = -392-4·(-12)·12
Δ = 2097
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:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{233}}{2*-12}=\frac{39-3\sqrt{233}}{-24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{233}}{2*-12}=\frac{39+3\sqrt{233}}{-24}
$