-3x+2=4x2

Solution for -3x+2=4x2 equation:

-3x+2=4x^2

We move all terms to the left:

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

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

a = -4; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-4)·2
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{41}}{2*-4}=\frac{3-\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*-4}=\frac{3+\sqrt{41}}{-8}
$