(4+x)(x+8)=10

Solution for (4+x)(x+8)=10 equation:

(4+x)(x+8)=10

We move all terms to the left:

(4+x)(x+8)-(10)=0

We add all the numbers together, and all the variables

(x+4)(x+8)-10=0

We multiply parentheses ..

(+x^2+8x+4x+32)-10=0

We get rid of parentheses

x^2+8x+4x+32-10=0

We add all the numbers together, and all the variables

x^2+12x+22=0

a = 1; b = 12; c = +22;
Δ = b2-4ac
Δ = 122-4·1·22
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{14}}{2*1}=\frac{-12-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{14}}{2*1}=\frac{-12+2\sqrt{14}}{2}
$