(14x-2)(3x+2)=3x

Solution for (14x-2)(3x+2)=3x equation:

(14x-2)(3x+2)=3x

We move all terms to the left:

(14x-2)(3x+2)-(3x)=0

We add all the numbers together, and all the variables

-3x+(14x-2)(3x+2)=0

We multiply parentheses ..

(+42x^2+28x-6x-4)-3x=0

We get rid of parentheses

42x^2+28x-6x-3x-4=0

We add all the numbers together, and all the variables

42x^2+19x-4=0

a = 42; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·42·(-4)
Δ = 1033
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{-(19)-\sqrt{1033}}{2*42}=\frac{-19-\sqrt{1033}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{1033}}{2*42}=\frac{-19+\sqrt{1033}}{84}
$