75=(1.5+.25x)(50-5x)

Solution for 75=(1.5+.25x)(50-5x) equation:

75=(1.5+.25x)(50-5x)

We move all terms to the left:

75-((1.5+.25x)(50-5x))=0

We add all the numbers together, and all the variables

-((.25x+1.5)(-5x+50))+75=0

We multiply parentheses ..

-((-5x^2+50x-7.5x+75))+75=0


We calculate terms in parentheses: -((-5x^2+50x-7.5x+75)), so:

(-5x^2+50x-7.5x+75)

We get rid of parentheses

-5x^2+50x-7.5x+75

We add all the numbers together, and all the variables

-5x^2+42.5x+75

Back to the equation:

-(-5x^2+42.5x+75)


We get rid of parentheses

5x^2-42.5x-75+75=0

We add all the numbers together, and all the variables

5x^2-42.5x=0

a = 5; b = -42.5; c = 0;
Δ = b2-4ac
Δ = -42.52-4·5·0
Δ = 1806.25
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{-(-42.5)-\sqrt{1806.25}}{2*5}=\frac{42.5-\sqrt{1806.25}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42.5)+\sqrt{1806.25}}{2*5}=\frac{42.5+\sqrt{1806.25}}{10}
$