10000000=6x^2-8x+2

Solution for 10000000=6x^2-8x+2 equation:

10000000=6x^2-8x+2

We move all terms to the left:

10000000-(6x^2-8x+2)=0

We get rid of parentheses

-6x^2+8x-2+10000000=0

We add all the numbers together, and all the variables

-6x^2+8x+9999998=0

a = -6; b = 8; c = +9999998;
Δ = b2-4ac
Δ = 82-4·(-6)·9999998
Δ = 240000016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240000016}=\sqrt{16*15000001}=\sqrt{16}*\sqrt{15000001}=4\sqrt{15000001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{15000001}}{2*-6}=\frac{-8-4\sqrt{15000001}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{15000001}}{2*-6}=\frac{-8+4\sqrt{15000001}}{-12}
$