2x(6x-3)=-4x(x-2.5)

Solution for 2x(6x-3)=-4x(x-2.5) equation:

2x(6x-3)=-4x(x-2.5)

We move all terms to the left:

2x(6x-3)-(-4x(x-2.5))=0

We multiply parentheses

12x^2-6x-(-4x(x-2.5))=0


We calculate terms in parentheses: -(-4x(x-2.5)), so:

-4x(x-2.5)

We multiply parentheses

-4x^2+10x

Back to the equation:

-(-4x^2+10x)


We get rid of parentheses

12x^2+4x^2-10x-6x=0

We add all the numbers together, and all the variables

16x^2-16x=0

a = 16; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·16·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*16}=\frac{32}{32}
=1
$