5(x+1)=2(5x+1)5x

Solution for 5(x+1)=2(5x+1)5x equation:

5(x+1)=2(5x+1)5x

We move all terms to the left:

5(x+1)-(2(5x+1)5x)=0

We multiply parentheses

5x-(2(5x+1)5x)+5=0


We calculate terms in parentheses: -(2(5x+1)5x), so:

2(5x+1)5x

We multiply parentheses

50x^2+10x

Back to the equation:

-(50x^2+10x)


We get rid of parentheses

-50x^2+5x-10x+5=0

We add all the numbers together, and all the variables

-50x^2-5x+5=0

a = -50; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-50)·5
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{41}}{2*-50}=\frac{5-5\sqrt{41}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{41}}{2*-50}=\frac{5+5\sqrt{41}}{-100}
$