20X+(15-X)*30X=15*20x

Solution for 20X+(15-X)*30X=15*20x equation:

20X+(15-X)*30X=15*20X

We move all terms to the left:

20X+(15-X)*30X-(15*20X)=0

We add all the numbers together, and all the variables

20X+(-1X+15)*30X-(+15*20X)=0

We multiply parentheses

-30X^2+20X+450X-(+15*20X)=0

We get rid of parentheses

-30X^2+20X+450X-15*20X=0

We add all the numbers together, and all the variables

-30X^2+470X-15*20X=0

Wy multiply elements

-30X^2+470X-300X=0

We add all the numbers together, and all the variables

-30X^2+170X=0

a = -30; b = 170; c = 0;
Δ = b2-4ac
Δ = 1702-4·(-30)·0
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-170}{2*-30}=\frac{-340}{-60}
=5+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+170}{2*-30}=\frac{0}{-60}
=0
$