10+t=2(t+13)t=

Solution for 10+t=2(t+13)t= equation:

10+t=2(t+13)t=

We move all terms to the left:

10+t-(2(t+13)t)=0


We calculate terms in parentheses: -(2(t+13)t), so:

2(t+13)t

We multiply parentheses

2t^2+26t

Back to the equation:

-(2t^2+26t)


We get rid of parentheses

-2t^2+t-26t+10=0

We add all the numbers together, and all the variables

-2t^2-25t+10=0

a = -2; b = -25; c = +10;
Δ = b2-4ac
Δ = -252-4·(-2)·10
Δ = 705
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{-(-25)-\sqrt{705}}{2*-2}=\frac{25-\sqrt{705}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{705}}{2*-2}=\frac{25+\sqrt{705}}{-4}
$