(x-150)(1-2/3)=250

Solution for (x-150)(1-2/3)=250 equation:

(x-150)(1-2/3)=250

We move all terms to the left:

(x-150)(1-2/3)-(250)=0

We add all the numbers together, and all the variables

(x-150)(-2/3+1)-250=0

We multiply parentheses ..

(-2x^2+x-150*-2/3-150)-250=0

We multiply all the terms by the denominator


(-2x^2+x-150*-2-250*3-150)=0

We get rid of parentheses

-2x^2+x-2-150-150*-250*3=0

We add all the numbers together, and all the variables

-2x^2+x+112348=0

a = -2; b = 1; c = +112348;
Δ = b2-4ac
Δ = 12-4·(-2)·112348
Δ = 898785
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:

$\sqrt{\Delta}=\sqrt{898785}=\sqrt{9*99865}=\sqrt{9}*\sqrt{99865}=3\sqrt{99865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{99865}}{2*-2}=\frac{-1-3\sqrt{99865}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{99865}}{2*-2}=\frac{-1+3\sqrt{99865}}{-4}
$