137.5=6x+1.5x^2

Solution for 137.5=6x+1.5x^2 equation:

137.5=6x+1.5x^2

We move all terms to the left:

137.5-(6x+1.5x^2)=0

We get rid of parentheses

-1.5x^2-6x+137.5=0

a = -1.5; b = -6; c = +137.5;
Δ = b2-4ac
Δ = -62-4·(-1.5)·137.5
Δ = 861
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{-(-6)-\sqrt{861}}{2*-1.5}=\frac{6-\sqrt{861}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{861}}{2*-1.5}=\frac{6+\sqrt{861}}{-3}
$