(x+10)(x+14)=(x+14)=(x+20)

Solution for (x+10)(x+14)=(x+14)=(x+20) equation:

(x+10)(x+14)=(x+14)=(x+20)

We move all terms to the left:

(x+10)(x+14)-((x+14))=0

We multiply parentheses ..

(+x^2+14x+10x+140)-((x+14))=0


We calculate terms in parentheses: -((x+14)), so:

(x+14)

We get rid of parentheses

x+14

Back to the equation:

-(x+14)


We get rid of parentheses

x^2+14x+10x-x+140-14=0

We add all the numbers together, and all the variables

x^2+23x+126=0

a = 1; b = 23; c = +126;
Δ = b2-4ac
Δ = 232-4·1·126
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5}{2*1}=\frac{-18}{2}
=-9
$