(1600+18x)(x-15)=(1200+22x)(x-20)

Solution for (1600+18x)(x-15)=(1200+22x)(x-20) equation:

(1600+18x)(x-15)=(1200+22x)(x-20)

We move all terms to the left:

(1600+18x)(x-15)-((1200+22x)(x-20))=0

We add all the numbers together, and all the variables

(18x+1600)(x-15)-((22x+1200)(x-20))=0

We multiply parentheses ..

(+18x^2-270x+1600x-24000)-((22x+1200)(x-20))=0


We calculate terms in parentheses: -((22x+1200)(x-20)), so:

(22x+1200)(x-20)

We multiply parentheses ..

(+22x^2-440x+1200x-24000)

We get rid of parentheses

22x^2-440x+1200x-24000

We add all the numbers together, and all the variables

22x^2+760x-24000

Back to the equation:

-(22x^2+760x-24000)


We get rid of parentheses

18x^2-22x^2-270x+1600x-760x-24000+24000=0

We add all the numbers together, and all the variables

-4x^2+570x=0

a = -4; b = 570; c = 0;
Δ = b2-4ac
Δ = 5702-4·(-4)·0
Δ = 324900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324900}=570$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(570)-570}{2*-4}=\frac{-1140}{-8}
=142+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(570)+570}{2*-4}=\frac{0}{-8}
=0
$