6x^2-15x+1=4x-2

Solution for 6x^2-15x+1=4x-2 equation:

6x^2-15x+1=4x-2

We move all terms to the left:

6x^2-15x+1-(4x-2)=0

We get rid of parentheses

6x^2-15x-4x+2+1=0

We add all the numbers together, and all the variables

6x^2-19x+3=0

a = 6; b = -19; c = +3;
Δ = b2-4ac
Δ = -192-4·6·3
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-17}{2*6}=\frac{2}{12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+17}{2*6}=\frac{36}{12}
=3
$