55/x=-49x+112

Solution for 55/x=-49x+112 equation:

55/x=-49x+112

We move all terms to the left:

55/x-(-49x+112)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

55/x+49x-112=0

We multiply all the terms by the denominator


49x*x-112*x+55=0

We add all the numbers together, and all the variables

-112x+49x*x+55=0

Wy multiply elements

49x^2-112x+55=0

a = 49; b = -112; c = +55;
Δ = b2-4ac
Δ = -1122-4·49·55
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{-(-112)-42}{2*49}=\frac{70}{98}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+42}{2*49}=\frac{154}{98}
=1+4/7
$