4x(x+7)=44

Solution for 4x(x+7)=44 equation:

4x(x+7)=44

We move all terms to the left:

4x(x+7)-(44)=0

We multiply parentheses

4x^2+28x-44=0

a = 4; b = 28; c = -44;
Δ = b2-4ac
Δ = 282-4·4·(-44)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{93}}{2*4}=\frac{-28-4\sqrt{93}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{93}}{2*4}=\frac{-28+4\sqrt{93}}{8}
$