1+3x=10x^2

Solution for 1+3x=10x^2 equation:

1+3x=10x^2

We move all terms to the left:

1+3x-(10x^2)=0

determiningTheFunctionDomain
-10x^2+3x+1=0

a = -10; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-10)·1
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*-10}=\frac{-10}{-20}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*-10}=\frac{4}{-20}
=-1/5
$