(100+2x)(150+x)=18000(100+2x)(150+x)=18000

Solution for (100+2x)(150+x)=18000(100+2x)(150+x)=18000 equation:

(100+2x)(150+x)=18000(100+2x)(150+x)=18000

We move all terms to the left:

(100+2x)(150+x)-(18000(100+2x)(150+x))=0

We add all the numbers together, and all the variables

(2x+100)(x+150)-(18000(2x+100)(x+150))=0

We multiply parentheses ..

(+2x^2+300x+100x+15000)-(18000(+2x^2+300x+100x+15000))=0


We calculate terms in parentheses: -(18000(+2x^2+300x+100x+15000)), so:

18000(+2x^2+300x+100x+15000)

We multiply parentheses

36000x^2+5400000x+1800000x+270000000

We add all the numbers together, and all the variables

36000x^2+7200000x+270000000

Back to the equation:

-(36000x^2+7200000x+270000000)


We get rid of parentheses

2x^2-36000x^2+300x+100x-7200000x+15000-270000000=0

We add all the numbers together, and all the variables

-35998x^2-7199600x-269985000=0

a = -35998; b = -7199600; c = -269985000;
Δ = b2-4ac
Δ = -71996002-4·(-35998)·(-269985000)
Δ = 12958560040000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12958560040000}=3599800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7199600)-3599800}{2*-35998}=\frac{3599800}{-71996}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7199600)+3599800}{2*-35998}=\frac{10799400}{-71996}
=-150
$