5(2+x)=-2(x-3)*5x

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

5(2+x)=-2(x-3)*5x

We move all terms to the left:

5(2+x)-(-2(x-3)*5x)=0

We add all the numbers together, and all the variables

5(x+2)-(-2(x-3)*5x)=0

We multiply parentheses

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


We calculate terms in parentheses: -(-2(x-3)*5x), so:

-2(x-3)*5x

We multiply parentheses

-10x^2+30x

Back to the equation:

-(-10x^2+30x)


We get rid of parentheses

10x^2-30x+5x+10=0

We add all the numbers together, and all the variables

10x^2-25x+10=0

a = 10; b = -25; c = +10;
Δ = b2-4ac
Δ = -252-4·10·10
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-15}{2*10}=\frac{10}{20}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+15}{2*10}=\frac{40}{20}
=2
$