8x2=6x-1

Solution for 8x2=6x-1 equation:

8x^2=6x-1

We move all terms to the left:

8x^2-(6x-1)=0

We get rid of parentheses

8x^2-6x+1=0

a = 8; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·8·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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