3(x+5)=4x(1+3x)

Solution for 3(x+5)=4x(1+3x) equation:

3(x+5)=4x(1+3x)

We move all terms to the left:

3(x+5)-(4x(1+3x))=0

We add all the numbers together, and all the variables

3(x+5)-(4x(3x+1))=0

We multiply parentheses

3x-(4x(3x+1))+15=0


We calculate terms in parentheses: -(4x(3x+1)), so:

4x(3x+1)

We multiply parentheses

12x^2+4x

Back to the equation:

-(12x^2+4x)


We get rid of parentheses

-12x^2+3x-4x+15=0

We add all the numbers together, and all the variables

-12x^2-1x+15=0

a = -12; b = -1; c = +15;
Δ = b2-4ac
Δ = -12-4·(-12)·15
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{721}}{2*-12}=\frac{1-\sqrt{721}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{721}}{2*-12}=\frac{1+\sqrt{721}}{-24}
$