0=x^2-150x+1875

Solution for 0=x^2-150x+1875 equation:

0=x^2-150x+1875

We move all terms to the left:

0-(x^2-150x+1875)=0

We add all the numbers together, and all the variables

-(x^2-150x+1875)=0

We get rid of parentheses

-x^2+150x-1875=0

We add all the numbers together, and all the variables

-1x^2+150x-1875=0

a = -1; b = 150; c = -1875;
Δ = b2-4ac
Δ = 1502-4·(-1)·(-1875)
Δ = 15000
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:

$\sqrt{\Delta}=\sqrt{15000}=\sqrt{2500*6}=\sqrt{2500}*\sqrt{6}=50\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-50\sqrt{6}}{2*-1}=\frac{-150-50\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+50\sqrt{6}}{2*-1}=\frac{-150+50\sqrt{6}}{-2}
$