50=t(7,5+t)

Solution for 50=t(7,5+t) equation:

50=t(7.5+t)

We move all terms to the left:

50-(t(7.5+t))=0

We add all the numbers together, and all the variables

-(t(t+7.5))+50=0


We calculate terms in parentheses: -(t(t+7.5)), so:

t(t+7.5)

We multiply parentheses

t^2+7.5t

Back to the equation:

-(t^2+7.5t)


We get rid of parentheses

-t^2-7.5t+50=0

We add all the numbers together, and all the variables

-1t^2-7.5t+50=0

a = -1; b = -7.5; c = +50;
Δ = b2-4ac
Δ = -7.52-4·(-1)·50
Δ = 256.25
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{-(-7.5)-\sqrt{256.25}}{2*-1}=\frac{7.5-\sqrt{256.25}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{256.25}}{2*-1}=\frac{7.5+\sqrt{256.25}}{-2}
$