3x=5-8x^2

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

3x=5-8x^2

We move all terms to the left:

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

We get rid of parentheses

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