(-42x+40x^2+2)/(-8x+2)=0

Solution for (-42x+40x^2+2)/(-8x+2)=0 equation:

(-42x+40x^2+2)/(-8x+2)=0


Domain of the equation: (-8x+2)!=0

We move all terms containing x to the left, all other terms to the right

-8x!=-2

x!=-2/-8

x!=1/4

x∈R


We multiply all the terms by the denominator


(-42x+40x^2+2)=0

We get rid of parentheses

40x^2-42x+2=0

a = 40; b = -42; c = +2;
Δ = b2-4ac
Δ = -422-4·40·2
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-38}{2*40}=\frac{4}{80}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+38}{2*40}=\frac{80}{80}
=1
$