12t=1/5t+12

Solution for 12t=1/5t+12 equation:

12t=1/5t+12

We move all terms to the left:

12t-(1/5t+12)=0


Domain of the equation: 5t+12)!=0

t∈R


We get rid of parentheses

12t-1/5t-12=0

We multiply all the terms by the denominator


12t*5t-12*5t-1=0

Wy multiply elements

60t^2-60t-1=0

a = 60; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·60·(-1)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{15}}{2*60}=\frac{60-16\sqrt{15}}{120}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{15}}{2*60}=\frac{60+16\sqrt{15}}{120}
$