(2x+10)(x-2)=(x+10)(x+10)

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

(2x+10)(x-2)=(x+10)(x+10)

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-4x+10x-20)-((x+10)(x+10))=0


We calculate terms in parentheses: -((x+10)(x+10)), so:

(x+10)(x+10)

We multiply parentheses ..

(+x^2+10x+10x+100)

We get rid of parentheses

x^2+10x+10x+100

We add all the numbers together, and all the variables

x^2+20x+100

Back to the equation:

-(x^2+20x+100)


We get rid of parentheses

2x^2-x^2-4x+10x-20x-20-100=0

We add all the numbers together, and all the variables

x^2-14x-120=0

a = 1; b = -14; c = -120;
Δ = b2-4ac
Δ = -142-4·1·(-120)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*1}=\frac{40}{2}
=20
$