150x-(3050+8x+0.1x^2)=0

Solution for 150x-(3050+8x+0.1x^2)=0 equation:

150x-(3050+8x+0.1x^2)=0

We get rid of parentheses

-0.1x^2-8x+150x-3050=0

We add all the numbers together, and all the variables

-0.1x^2+142x-3050=0

a = -0.1; b = 142; c = -3050;
Δ = b2-4ac
Δ = 1422-4·(-0.1)·(-3050)
Δ = 18944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18944}=\sqrt{256*74}=\sqrt{256}*\sqrt{74}=16\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(142)-16\sqrt{74}}{2*-0.1}=\frac{-142-16\sqrt{74}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(142)+16\sqrt{74}}{2*-0.1}=\frac{-142+16\sqrt{74}}{-0.2}
$