6x+4+5x(x+6)=56

Solution for 6x+4+5x(x+6)=56 equation:

6x+4+5x(x+6)=56

We move all terms to the left:

6x+4+5x(x+6)-(56)=0

We add all the numbers together, and all the variables

6x+5x(x+6)-52=0

We multiply parentheses

5x^2+6x+30x-52=0

We add all the numbers together, and all the variables

5x^2+36x-52=0

a = 5; b = 36; c = -52;
Δ = b2-4ac
Δ = 362-4·5·(-52)
Δ = 2336
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:

$\sqrt{\Delta}=\sqrt{2336}=\sqrt{16*146}=\sqrt{16}*\sqrt{146}=4\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{146}}{2*5}=\frac{-36-4\sqrt{146}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{146}}{2*5}=\frac{-36+4\sqrt{146}}{10}
$