90=(5t+30)(t+3)

Solution for 90=(5t+30)(t+3) equation:

90=(5t+30)(t+3)

We move all terms to the left:

90-((5t+30)(t+3))=0

We multiply parentheses ..

-((+5t^2+15t+30t+90))+90=0


We calculate terms in parentheses: -((+5t^2+15t+30t+90)), so:

(+5t^2+15t+30t+90)

We get rid of parentheses

5t^2+15t+30t+90

We add all the numbers together, and all the variables

5t^2+45t+90

Back to the equation:

-(5t^2+45t+90)


We get rid of parentheses

-5t^2-45t-90+90=0

We add all the numbers together, and all the variables

-5t^2-45t=0

a = -5; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·(-5)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*-5}=\frac{0}{-10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*-5}=\frac{90}{-10}
=-9
$