6x^2=x^2-14x+3

Solution for 6x^2=x^2-14x+3 equation:

6x^2=x^2-14x+3

We move all terms to the left:

6x^2-(x^2-14x+3)=0

We get rid of parentheses

6x^2-x^2+14x-3=0

We add all the numbers together, and all the variables

5x^2+14x-3=0

a = 5; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·5·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16}{2*5}=\frac{2}{10}
=1/5
$