92-42x=2x^2

Solution for 92-42x=2x^2 equation:

92-42x=2x^2

We move all terms to the left:

92-42x-(2x^2)=0

determiningTheFunctionDomain
-2x^2-42x+92=0

a = -2; b = -42; c = +92;
Δ = b2-4ac
Δ = -422-4·(-2)·92
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-50}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+50}{2*-2}=\frac{92}{-4}
=-23
$