2-7x=4x^2

Solution for 2-7x=4x^2 equation:

2-7x=4x^2

We move all terms to the left:

2-7x-(4x^2)=0

determiningTheFunctionDomain
-4x^2-7x+2=0

a = -4; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-4)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-4}=\frac{16}{-8}
=-2
$