4x(2x-3)-5(1-6x)=15x-3x(7-8x)

Solution for 4x(2x-3)-5(1-6x)=15x-3x(7-8x) equation:

4x(2x-3)-5(1-6x)=15x-3x(7-8x)

We move all terms to the left:

4x(2x-3)-5(1-6x)-(15x-3x(7-8x))=0

We add all the numbers together, and all the variables

4x(2x-3)-5(-6x+1)-(15x-3x(-8x+7))=0

We multiply parentheses

8x^2-12x+30x-(15x-3x(-8x+7))-5=0


We calculate terms in parentheses: -(15x-3x(-8x+7)), so:

15x-3x(-8x+7)

We multiply parentheses

24x^2+15x-21x

We add all the numbers together, and all the variables

24x^2-6x

Back to the equation:

-(24x^2-6x)


We add all the numbers together, and all the variables

8x^2+18x-(24x^2-6x)-5=0

We get rid of parentheses

8x^2-24x^2+18x+6x-5=0

We add all the numbers together, and all the variables

-16x^2+24x-5=0

a = -16; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·(-16)·(-5)
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{-(24)-16}{2*-16}=\frac{-40}{-32}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16}{2*-16}=\frac{-8}{-32}
=1/4
$