0.4x(5x-15)=2.5x(x+3)

Solution for 0.4x(5x-15)=2.5x(x+3) equation:

0.4x(5x-15)=2.5x(x+3)

We move all terms to the left:

0.4x(5x-15)-(2.5x(x+3))=0

We multiply parentheses

0x^2+0x-(2.5x(x+3))=0


We calculate terms in parentheses: -(2.5x(x+3)), so:

2.5x(x+3)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We add all the numbers together, and all the variables

x^2+x-(2x^2+6x)=0

We get rid of parentheses

x^2-2x^2+x-6x=0

We add all the numbers together, and all the variables

-1x^2-5x=0

a = -1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-1}=\frac{10}{-2}
=-5
$