56x=(10x-2)(5x+3)

Solution for 56x=(10x-2)(5x+3) equation:

56x=(10x-2)(5x+3)

We move all terms to the left:

56x-((10x-2)(5x+3))=0

We multiply parentheses ..

-((+50x^2+30x-10x-6))+56x=0


We calculate terms in parentheses: -((+50x^2+30x-10x-6)), so:

(+50x^2+30x-10x-6)

We get rid of parentheses

50x^2+30x-10x-6

We add all the numbers together, and all the variables

50x^2+20x-6

Back to the equation:

-(50x^2+20x-6)


We add all the numbers together, and all the variables

56x-(50x^2+20x-6)=0

We get rid of parentheses

-50x^2+56x-20x+6=0

We add all the numbers together, and all the variables

-50x^2+36x+6=0

a = -50; b = 36; c = +6;
Δ = b2-4ac
Δ = 362-4·(-50)·6
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{39}}{2*-50}=\frac{-36-8\sqrt{39}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{39}}{2*-50}=\frac{-36+8\sqrt{39}}{-100}
$