90(t+10.5)2t=180

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

90(t+10.5)2t=180

We move all terms to the left:

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

We multiply parentheses

180t^2+1890t-180=0

a = 180; b = 1890; c = -180;
Δ = b2-4ac
Δ = 18902-4·180·(-180)
Δ = 3701700
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:

$\sqrt{\Delta}=\sqrt{3701700}=\sqrt{8100*457}=\sqrt{8100}*\sqrt{457}=90\sqrt{457}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1890)-90\sqrt{457}}{2*180}=\frac{-1890-90\sqrt{457}}{360}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1890)+90\sqrt{457}}{2*180}=\frac{-1890+90\sqrt{457}}{360}
$