2t(t+10.5)+90=180

Solution for 2t(t+10.5)+90=180 equation:

2t(t+10.5)+90=180

We move all terms to the left:

2t(t+10.5)+90-(180)=0

We add all the numbers together, and all the variables

2t(t+10.5)-90=0

We multiply parentheses

2t^2+21t-90=0

a = 2; b = 21; c = -90;
Δ = b2-4ac
Δ = 212-4·2·(-90)
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{129}}{2*2}=\frac{-21-3\sqrt{129}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{129}}{2*2}=\frac{-21+3\sqrt{129}}{4}
$