8x+6=4x^2-3

Solution for 8x+6=4x^2-3 equation:

8x+6=4x^2-3

We move all terms to the left:

8x+6-(4x^2-3)=0

We get rid of parentheses

-4x^2+8x+3+6=0

We add all the numbers together, and all the variables

-4x^2+8x+9=0

a = -4; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-4)·9
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{13}}{2*-4}=\frac{-8-4\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{13}}{2*-4}=\frac{-8+4\sqrt{13}}{-8}
$