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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(4x(x+5)), so:

4x(x+5)

We multiply parentheses

4x^2+20x

Back to the equation:

-(4x^2+20x)


We get rid of parentheses

-4x^2+3x-20x+6=0

We add all the numbers together, and all the variables

-4x^2-17x+6=0

a = -4; b = -17; c = +6;
Δ = b2-4ac
Δ = -172-4·(-4)·6
Δ = 385
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{-(-17)-\sqrt{385}}{2*-4}=\frac{17-\sqrt{385}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{385}}{2*-4}=\frac{17+\sqrt{385}}{-8}
$