8x(x-1)=(x^2)+3

Solution for 8x(x-1)=(x^2)+3 equation:

8x(x-1)=(x^2)+3

We move all terms to the left:

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

We multiply parentheses

8x^2-8x-(x^2+3)=0

We get rid of parentheses

8x^2-x^2-8x-3=0

We add all the numbers together, and all the variables

7x^2-8x-3=0

a = 7; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·7·(-3)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{37}}{2*7}=\frac{8-2\sqrt{37}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{37}}{2*7}=\frac{8+2\sqrt{37}}{14}
$