3x(90-x)=x-40

Solution for 3x(90-x)=x-40 equation:

3x(90-x)=x-40

We move all terms to the left:

3x(90-x)-(x-40)=0

We add all the numbers together, and all the variables

3x(-1x+90)-(x-40)=0

We multiply parentheses

-3x^2+270x-(x-40)=0

We get rid of parentheses

-3x^2+270x-x+40=0

We add all the numbers together, and all the variables

-3x^2+269x+40=0

a = -3; b = 269; c = +40;
Δ = b2-4ac
Δ = 2692-4·(-3)·40
Δ = 72841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(269)-\sqrt{72841}}{2*-3}=\frac{-269-\sqrt{72841}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(269)+\sqrt{72841}}{2*-3}=\frac{-269+\sqrt{72841}}{-6}
$