4x(4+x)-6=30

Solution for 4x(4+x)-6=30 equation:

4x(4+x)-6=30

We move all terms to the left:

4x(4+x)-6-(30)=0

We add all the numbers together, and all the variables

4x(x+4)-6-30=0

We add all the numbers together, and all the variables

4x(x+4)-36=0

We multiply parentheses

4x^2+16x-36=0

a = 4; b = 16; c = -36;
Δ = b2-4ac
Δ = 162-4·4·(-36)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{13}}{2*4}=\frac{-16-8\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{13}}{2*4}=\frac{-16+8\sqrt{13}}{8}
$