4x(7+x)=55

Solution for 4x(7+x)=55 equation:

4x(7+x)=55

We move all terms to the left:

4x(7+x)-(55)=0

We add all the numbers together, and all the variables

4x(x+7)-55=0

We multiply parentheses

4x^2+28x-55=0

a = 4; b = 28; c = -55;
Δ = b2-4ac
Δ = 282-4·4·(-55)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8\sqrt{26}}{2*4}=\frac{-28-8\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8\sqrt{26}}{2*4}=\frac{-28+8\sqrt{26}}{8}
$