x+3/42x=90

Solution for x+3/42x=90 equation:

x+3/42x=90

We move all terms to the left:

x+3/42x-(90)=0


Domain of the equation: 42x!=0

x!=0/42

x!=0

x∈R


We multiply all the terms by the denominator


x*42x-90*42x+3=0

Wy multiply elements

42x^2-3780x+3=0

a = 42; b = -3780; c = +3;
Δ = b2-4ac
Δ = -37802-4·42·3
Δ = 14287896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14287896}=\sqrt{36*396886}=\sqrt{36}*\sqrt{396886}=6\sqrt{396886}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3780)-6\sqrt{396886}}{2*42}=\frac{3780-6\sqrt{396886}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3780)+6\sqrt{396886}}{2*42}=\frac{3780+6\sqrt{396886}}{84}
$