3(2x-8)=5x(28-2x)

Solution for 3(2x-8)=5x(28-2x) equation:

3(2x-8)=5x(28-2x)

We move all terms to the left:

3(2x-8)-(5x(28-2x))=0

We add all the numbers together, and all the variables

3(2x-8)-(5x(-2x+28))=0

We multiply parentheses

6x-(5x(-2x+28))-24=0


We calculate terms in parentheses: -(5x(-2x+28)), so:

5x(-2x+28)

We multiply parentheses

-10x^2+140x

Back to the equation:

-(-10x^2+140x)


We get rid of parentheses

10x^2-140x+6x-24=0

We add all the numbers together, and all the variables

10x^2-134x-24=0

a = 10; b = -134; c = -24;
Δ = b2-4ac
Δ = -1342-4·10·(-24)
Δ = 18916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18916}=\sqrt{4*4729}=\sqrt{4}*\sqrt{4729}=2\sqrt{4729}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-2\sqrt{4729}}{2*10}=\frac{134-2\sqrt{4729}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+2\sqrt{4729}}{2*10}=\frac{134+2\sqrt{4729}}{20}
$