5x(3x+6)+4(6x+4)+6=39x+52

Solution for 5x(3x+6)+4(6x+4)+6=39x+52 equation:

5x(3x+6)+4(6x+4)+6=39x+52

We move all terms to the left:

5x(3x+6)+4(6x+4)+6-(39x+52)=0

We multiply parentheses

15x^2+30x+24x-(39x+52)+16+6=0

We get rid of parentheses

15x^2+30x+24x-39x-52+16+6=0

We add all the numbers together, and all the variables

15x^2+15x-30=0

a = 15; b = 15; c = -30;
Δ = b2-4ac
Δ = 152-4·15·(-30)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-45}{2*15}=\frac{-60}{30}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+45}{2*15}=\frac{30}{30}
=1
$