2(5+t)6t=t+22

Solution for 2(5+t)6t=t+22 equation:

2(5+t)6t=t+22

We move all terms to the left:

2(5+t)6t-(t+22)=0

We add all the numbers together, and all the variables

2(t+5)6t-(t+22)=0

We multiply parentheses

12t^2+60t-(t+22)=0

We get rid of parentheses

12t^2+60t-t-22=0

We add all the numbers together, and all the variables

12t^2+59t-22=0

a = 12; b = 59; c = -22;
Δ = b2-4ac
Δ = 592-4·12·(-22)
Δ = 4537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-\sqrt{4537}}{2*12}=\frac{-59-\sqrt{4537}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+\sqrt{4537}}{2*12}=\frac{-59+\sqrt{4537}}{24}
$