6+2(x-5)x+4=44

Solution for 6+2(x-5)x+4=44 equation:

6+2(x-5)x+4=44

We move all terms to the left:

6+2(x-5)x+4-(44)=0

We add all the numbers together, and all the variables

2(x-5)x-34=0

We multiply parentheses

2x^2-10x-34=0

a = 2; b = -10; c = -34;
Δ = b2-4ac
Δ = -102-4·2·(-34)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{93}}{2*2}=\frac{10-2\sqrt{93}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{93}}{2*2}=\frac{10+2\sqrt{93}}{4}
$