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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2-18x-(5x-4)+2=0

We get rid of parentheses

3x^2-18x-5x+4+2=0

We add all the numbers together, and all the variables

3x^2-23x+6=0

a = 3; b = -23; c = +6;
Δ = b2-4ac
Δ = -232-4·3·6
Δ = 457
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{-(-23)-\sqrt{457}}{2*3}=\frac{23-\sqrt{457}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{457}}{2*3}=\frac{23+\sqrt{457}}{6}
$