t+(t-35)+(t-46)+1/2t=360

Solution for t+(t-35)+(t-46)+1/2t=360 equation:

t+(t-35)+(t-46)+1/2t=360

We move all terms to the left:

t+(t-35)+(t-46)+1/2t-(360)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We get rid of parentheses

t+t+t+1/2t-35-46-360=0

We multiply all the terms by the denominator


t*2t+t*2t+t*2t-35*2t-46*2t-360*2t+1=0

Wy multiply elements

2t^2+2t^2+2t^2-70t-92t-720t+1=0

We add all the numbers together, and all the variables

6t^2-882t+1=0

a = 6; b = -882; c = +1;
Δ = b2-4ac
Δ = -8822-4·6·1
Δ = 777900
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:

$\sqrt{\Delta}=\sqrt{777900}=\sqrt{100*7779}=\sqrt{100}*\sqrt{7779}=10\sqrt{7779}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-882)-10\sqrt{7779}}{2*6}=\frac{882-10\sqrt{7779}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-882)+10\sqrt{7779}}{2*6}=\frac{882+10\sqrt{7779}}{12}
$