4x(x+8)=7+4x

Solution for 4x(x+8)=7+4x equation:

4x(x+8)=7+4x

We move all terms to the left:

4x(x+8)-(7+4x)=0

We add all the numbers together, and all the variables

4x(x+8)-(4x+7)=0

We multiply parentheses

4x^2+32x-(4x+7)=0

We get rid of parentheses

4x^2+32x-4x-7=0

We add all the numbers together, and all the variables

4x^2+28x-7=0

a = 4; b = 28; c = -7;
Δ = b2-4ac
Δ = 282-4·4·(-7)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8\sqrt{14}}{2*4}=\frac{-28-8\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8\sqrt{14}}{2*4}=\frac{-28+8\sqrt{14}}{8}
$