5X(10+5x)=5(20+10x)

Solution for 5X(10+5x)=5(20+10x) equation:

5X(10+5X)=5(20+10X)

We move all terms to the left:

5X(10+5X)-(5(20+10X))=0

We add all the numbers together, and all the variables

5X(5X+10)-(5(10X+20))=0

We multiply parentheses

25X^2+50X-(5(10X+20))=0


We calculate terms in parentheses: -(5(10X+20)), so:

5(10X+20)

We multiply parentheses

50X+100

Back to the equation:

-(50X+100)


We get rid of parentheses

25X^2+50X-50X-100=0

We add all the numbers together, and all the variables

25X^2-100=0

a = 25; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·25·(-100)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*25}=\frac{-100}{50}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*25}=\frac{100}{50}
=2
$