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

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

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

We move all terms to the left:

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

We multiply parentheses

12x^2+8x+10x-(5(2x+4))-12=0


We calculate terms in parentheses: -(5(2x+4)), so:

5(2x+4)

We multiply parentheses

10x+20

Back to the equation:

-(10x+20)


We add all the numbers together, and all the variables

12x^2+18x-(10x+20)-12=0

We get rid of parentheses

12x^2+18x-10x-20-12=0

We add all the numbers together, and all the variables

12x^2+8x-32=0

a = 12; b = 8; c = -32;
Δ = b2-4ac
Δ = 82-4·12·(-32)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-40}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+40}{2*12}=\frac{32}{24}
=1+1/3
$