2(x+5)=5x(x-4)

Solution for 2(x+5)=5x(x-4) equation:

2(x+5)=5x(x-4)

We move all terms to the left:

2(x+5)-(5x(x-4))=0

We multiply parentheses

2x-(5x(x-4))+10=0


We calculate terms in parentheses: -(5x(x-4)), so:

5x(x-4)

We multiply parentheses

5x^2-20x

Back to the equation:

-(5x^2-20x)


We get rid of parentheses

-5x^2+2x+20x+10=0

We add all the numbers together, and all the variables

-5x^2+22x+10=0

a = -5; b = 22; c = +10;
Δ = b2-4ac
Δ = 222-4·(-5)·10
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{19}}{2*-5}=\frac{-22-6\sqrt{19}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{19}}{2*-5}=\frac{-22+6\sqrt{19}}{-10}
$