4x(3x+5)=14x+12-2x+8

Solution for 4x(3x+5)=14x+12-2x+8 equation:

4x(3x+5)=14x+12-2x+8

We move all terms to the left:

4x(3x+5)-(14x+12-2x+8)=0

We add all the numbers together, and all the variables

4x(3x+5)-(12x+20)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+8x-20=0

a = 12; b = 8; c = -20;
Δ = b2-4ac
Δ = 82-4·12·(-20)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-32}{2*12}=\frac{-40}{24}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+32}{2*12}=\frac{24}{24}
=1
$