60(x)=60(x+15)-2x(x+15)

Solution for 60(x)=60(x+15)-2x(x+15) equation:

60(x)=60(x+15)-2x(x+15)

We move all terms to the left:

60(x)-(60(x+15)-2x(x+15))=0


We calculate terms in parentheses: -(60(x+15)-2x(x+15)), so:

60(x+15)-2x(x+15)

We multiply parentheses

-2x^2+60x-30x+900

We add all the numbers together, and all the variables

-2x^2+30x+900

Back to the equation:

-(-2x^2+30x+900)


We get rid of parentheses

2x^2-30x+60x-900=0

We add all the numbers together, and all the variables

2x^2+30x-900=0

a = 2; b = 30; c = -900;
Δ = b2-4ac
Δ = 302-4·2·(-900)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-90}{2*2}=\frac{-120}{4}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+90}{2*2}=\frac{60}{4}
=15
$