3x(180-x)=2x(90-x)

Solution for 3x(180-x)=2x(90-x) equation:

3x(180-x)=2x(90-x)

We move all terms to the left:

3x(180-x)-(2x(90-x))=0

We add all the numbers together, and all the variables

3x(-1x+180)-(2x(-1x+90))=0

We multiply parentheses

-3x^2+540x-(2x(-1x+90))=0


We calculate terms in parentheses: -(2x(-1x+90)), so:

2x(-1x+90)

We multiply parentheses

-2x^2+180x

Back to the equation:

-(-2x^2+180x)


We get rid of parentheses

-3x^2+2x^2-180x+540x=0

We add all the numbers together, and all the variables

-1x^2+360x=0

a = -1; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·(-1)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*-1}=\frac{-720}{-2}
=+360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*-1}=\frac{0}{-2}
=0
$