2-3x=5x^2

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

2-3x=5x^2

We move all terms to the left:

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

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

a = -5; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-5)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*-5}=\frac{-4}{-10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*-5}=\frac{10}{-10}
=-1
$