6x+8=8x^2

Solution for 6x+8=8x^2 equation:

6x+8=8x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-8x^2+6x+8=0

a = -8; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-8)·8
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{73}}{2*-8}=\frac{-6-2\sqrt{73}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{73}}{2*-8}=\frac{-6+2\sqrt{73}}{-16}
$