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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2.5(x+3)

We multiply parentheses

2.5x+7.5

Back to the equation:

-(2.5x+7.5)


We add all the numbers together, and all the variables

x^2+x-(2.5x+7.5)=0

We get rid of parentheses

x^2+x-2.5x-7.5=0

We add all the numbers together, and all the variables

x^2-1.5x-7.5=0

a = 1; b = -1.5; c = -7.5;
Δ = b2-4ac
Δ = -1.52-4·1·(-7.5)
Δ = 32.25
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{-(-1.5)-\sqrt{32.25}}{2*1}=\frac{1.5-\sqrt{32.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{32.25}}{2*1}=\frac{1.5+\sqrt{32.25}}{2}
$