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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-15x-4=0

a = 4; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·4·(-4)
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{-(-15)-17}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+17}{2*4}=\frac{32}{8}
=4
$