(x+2)(x+10)=(x+14)(10)

Solution for (x+2)(x+10)=(x+14)(10) equation:

(x+2)(x+10)=(x+14)(10)

We move all terms to the left:

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

We multiply parentheses ..

(+x^2+10x+2x+20)-((x+14)10)=0


We calculate terms in parentheses: -((x+14)10), so:

(x+14)10

We multiply parentheses

10x+140

Back to the equation:

-(10x+140)


We get rid of parentheses

x^2+10x+2x-10x+20-140=0

We add all the numbers together, and all the variables

x^2+2x-120=0

a = 1; b = 2; c = -120;
Δ = b2-4ac
Δ = 22-4·1·(-120)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*1}=\frac{20}{2}
=10
$