45000=30x^2-1950x

Solution for 45000=30x^2-1950x equation:

45000=30x^2-1950x

We move all terms to the left:

45000-(30x^2-1950x)=0

We get rid of parentheses

-30x^2+1950x+45000=0

a = -30; b = 1950; c = +45000;
Δ = b2-4ac
Δ = 19502-4·(-30)·45000
Δ = 9202500
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:

$\sqrt{\Delta}=\sqrt{9202500}=\sqrt{22500*409}=\sqrt{22500}*\sqrt{409}=150\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1950)-150\sqrt{409}}{2*-30}=\frac{-1950-150\sqrt{409}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1950)+150\sqrt{409}}{2*-30}=\frac{-1950+150\sqrt{409}}{-60}
$