10x-8x^2-1=3x-2x^2-1

Solution for 10x-8x^2-1=3x-2x^2-1 equation:

10x-8x^2-1=3x-2x^2-1

We move all terms to the left:

10x-8x^2-1-(3x-2x^2-1)=0

We get rid of parentheses

-8x^2+2x^2-3x+10x+1-1=0

We add all the numbers together, and all the variables

-6x^2+7x=0

a = -6; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-6)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-6}=\frac{-14}{-12}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-6}=\frac{0}{-12}
=0
$