1=3x+4x^2

Solution for 1=3x+4x^2 equation:

1=3x+4x^2

We move all terms to the left:

1-(3x+4x^2)=0

We get rid of parentheses

-4x^2-3x+1=0

a = -4; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-4)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-4}=\frac{8}{-8}
=-1
$