5-3x=8x^2

Solution for 5-3x=8x^2 equation:

5-3x=8x^2

We move all terms to the left:

5-3x-(8x^2)=0

determiningTheFunctionDomain
-8x^2-3x+5=0

a = -8; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-8)·5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*-8}=\frac{-10}{-16}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*-8}=\frac{16}{-16}
=-1
$