(2x+10)(x+6)=258+2x

Solution for (2x+10)(x+6)=258+2x equation:

(2x+10)(x+6)=258+2x

We move all terms to the left:

(2x+10)(x+6)-(258+2x)=0

We add all the numbers together, and all the variables

(2x+10)(x+6)-(2x+258)=0

We get rid of parentheses

(2x+10)(x+6)-2x-258=0

We multiply parentheses ..

(+2x^2+12x+10x+60)-2x-258=0

We get rid of parentheses

2x^2+12x+10x-2x+60-258=0

We add all the numbers together, and all the variables

2x^2+20x-198=0

a = 2; b = 20; c = -198;
Δ = b2-4ac
Δ = 202-4·2·(-198)
Δ = 1984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{31}}{2*2}=\frac{-20-8\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{31}}{2*2}=\frac{-20+8\sqrt{31}}{4}
$