6x(3-4x)=-x(5x-1)

Solution for 6x(3-4x)=-x(5x-1) equation:

6x(3-4x)=-x(5x-1)

We move all terms to the left:

6x(3-4x)-(-x(5x-1))=0

We add all the numbers together, and all the variables

6x(-4x+3)-(-x(5x-1))=0

We multiply parentheses

-24x^2+18x-(-x(5x-1))=0


We calculate terms in parentheses: -(-x(5x-1)), so:

-x(5x-1)

We multiply parentheses

-5x^2+1x

We add all the numbers together, and all the variables

-5x^2+x

Back to the equation:

-(-5x^2+x)


We get rid of parentheses

-24x^2+5x^2-x+18x=0

We add all the numbers together, and all the variables

-19x^2+17x=0

a = -19; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-19)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-19}=\frac{-34}{-38}
=17/19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-19}=\frac{0}{-38}
=0
$