70x/(x^2+49)=4

Solution for 70x/(x^2+49)=4 equation:

70x/(x^2+49)=4

We move all terms to the left:

70x/(x^2+49)-(4)=0


Domain of the equation: (x^2+49)!=0

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

x^2!=-49

x^2!=-49/

x^2!=√-1/0

x!=NAN

x∈R


We multiply all the terms by the denominator


70x-4*(x^2+49)=0

We multiply parentheses

-4x^2+70x-196=0

a = -4; b = 70; c = -196;
Δ = b2-4ac
Δ = 702-4·(-4)·(-196)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-42}{2*-4}=\frac{-112}{-8}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+42}{2*-4}=\frac{-28}{-8}
=3+1/2
$