-5t(t+6)=5(4-t)

Solution for -5t(t+6)=5(4-t) equation:

-5t(t+6)=5(4-t)

We move all terms to the left:

-5t(t+6)-(5(4-t))=0

We add all the numbers together, and all the variables

-5t(t+6)-(5(-1t+4))=0

We multiply parentheses

-5t^2-30t-(5(-1t+4))=0


We calculate terms in parentheses: -(5(-1t+4)), so:

5(-1t+4)

We multiply parentheses

-5t+20

Back to the equation:

-(-5t+20)


We get rid of parentheses

-5t^2-30t+5t-20=0

We add all the numbers together, and all the variables

-5t^2-25t-20=0

a = -5; b = -25; c = -20;
Δ = b2-4ac
Δ = -252-4·(-5)·(-20)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-15}{2*-5}=\frac{10}{-10}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+15}{2*-5}=\frac{40}{-10}
=-4
$