400x-6x^2=180+1350

Solution for 400x-6x^2=180+1350 equation:

400x-6x^2=180+1350

We move all terms to the left:

400x-6x^2-(180+1350)=0

We add all the numbers together, and all the variables

-6x^2+400x-1530=0

a = -6; b = 400; c = -1530;
Δ = b2-4ac
Δ = 4002-4·(-6)·(-1530)
Δ = 123280
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:

$\sqrt{\Delta}=\sqrt{123280}=\sqrt{16*7705}=\sqrt{16}*\sqrt{7705}=4\sqrt{7705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-4\sqrt{7705}}{2*-6}=\frac{-400-4\sqrt{7705}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+4\sqrt{7705}}{2*-6}=\frac{-400+4\sqrt{7705}}{-12}
$