6x2-15x+2=2x2+10x-4

Solution for 6x2-15x+2=2x2+10x-4 equation:

6x^2-15x+2=2x^2+10x-4

We move all terms to the left:

6x^2-15x+2-(2x^2+10x-4)=0

We get rid of parentheses

6x^2-2x^2-15x-10x+4+2=0

We add all the numbers together, and all the variables

4x^2-25x+6=0

a = 4; b = -25; c = +6;
Δ = b2-4ac
Δ = -252-4·4·6
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-23}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+23}{2*4}=\frac{48}{8}
=6
$