4*6=3x(3+2x+5)

Solution for 4*6=3x(3+2x+5) equation:

4*6=3x(3+2x+5)

We move all terms to the left:

4*6-(3x(3+2x+5))=0

We add all the numbers together, and all the variables

-(3x(2x+8))+4*6=0

We add all the numbers together, and all the variables

-(3x(2x+8))+24=0


We calculate terms in parentheses: -(3x(2x+8)), so:

3x(2x+8)

We multiply parentheses

6x^2+24x

Back to the equation:

-(6x^2+24x)


We get rid of parentheses

-6x^2-24x+24=0

a = -6; b = -24; c = +24;
Δ = b2-4ac
Δ = -242-4·(-6)·24
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*-6}=\frac{24-24\sqrt{2}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*-6}=\frac{24+24\sqrt{2}}{-12}
$