X=4b^2+8b+3

Solution for X=4b^2+8b+3 equation:

X=4X^2+8X+3

We move all terms to the left:

X-(4X^2+8X+3)=0

We get rid of parentheses

-4X^2+X-8X-3=0

We add all the numbers together, and all the variables

-4X^2-7X-3=0

a = -4; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·(-4)·(-3)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*-4}=\frac{6}{-8}
=-3/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*-4}=\frac{8}{-8}
=-1
$