2-5(t-3)+t=7t(6t+8)

Solution for 2-5(t-3)+t=7t(6t+8) equation:

2-5(t-3)+t=7t(6t+8)

We move all terms to the left:

2-5(t-3)+t-(7t(6t+8))=0

We add all the numbers together, and all the variables

t-5(t-3)-(7t(6t+8))+2=0

We multiply parentheses

t-5t-(7t(6t+8))+15+2=0


We calculate terms in parentheses: -(7t(6t+8)), so:

7t(6t+8)

We multiply parentheses

42t^2+56t

Back to the equation:

-(42t^2+56t)


We add all the numbers together, and all the variables

-4t-(42t^2+56t)+17=0

We get rid of parentheses

-42t^2-4t-56t+17=0

We add all the numbers together, and all the variables

-42t^2-60t+17=0

a = -42; b = -60; c = +17;
Δ = b2-4ac
Δ = -602-4·(-42)·17
Δ = 6456
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:

$\sqrt{\Delta}=\sqrt{6456}=\sqrt{4*1614}=\sqrt{4}*\sqrt{1614}=2\sqrt{1614}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{1614}}{2*-42}=\frac{60-2\sqrt{1614}}{-84}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{1614}}{2*-42}=\frac{60+2\sqrt{1614}}{-84}
$