(x+3)(2x+8)-42=0/2

Solution for (x+3)(2x+8)-42=0/2 equation:

(x+3)(2x+8)-42=0/2

We move all terms to the left:

(x+3)(2x+8)-42-(0/2)=0

We add all the numbers together, and all the variables

(x+3)(2x+8)-42-0=0

We add all the numbers together, and all the variables

(x+3)(2x+8)-42=0

We multiply parentheses ..

(+2x^2+8x+6x+24)-42=0

We get rid of parentheses

2x^2+8x+6x+24-42=0

We add all the numbers together, and all the variables

2x^2+14x-18=0

a = 2; b = 14; c = -18;
Δ = b2-4ac
Δ = 142-4·2·(-18)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{85}}{2*2}=\frac{-14-2\sqrt{85}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{85}}{2*2}=\frac{-14+2\sqrt{85}}{4}
$