t+5=1/10t+14

Solution for t+5=1/10t+14 equation:

t+5=1/10t+14

We move all terms to the left:

t+5-(1/10t+14)=0


Domain of the equation: 10t+14)!=0

t∈R


We get rid of parentheses

t-1/10t-14+5=0

We multiply all the terms by the denominator


t*10t-14*10t+5*10t-1=0

Wy multiply elements

10t^2-140t+50t-1=0

We add all the numbers together, and all the variables

10t^2-90t-1=0

a = 10; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·10·(-1)
Δ = 8140
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:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2035}}{2*10}=\frac{90-2\sqrt{2035}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2035}}{2*10}=\frac{90+2\sqrt{2035}}{20}
$