69=180x+0.01x^2+x+60

Solution for 69=180x+0.01x^2+x+60 equation:

69=180x+0.01x^2+x+60

We move all terms to the left:

69-(180x+0.01x^2+x+60)=0

We get rid of parentheses

-0.01x^2-180x-x-60+69=0

We add all the numbers together, and all the variables

-0.01x^2-181x+9=0

a = -0.01; b = -181; c = +9;
Δ = b2-4ac
Δ = -1812-4·(-0.01)·9
Δ = 32761.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-181)-\sqrt{32761.36}}{2*-0.01}=\frac{181-\sqrt{32761.36}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-181)+\sqrt{32761.36}}{2*-0.01}=\frac{181+\sqrt{32761.36}}{-0.02}
$