2x-14/5x+2=-1

Solution for 2x-14/5x+2=-1 equation:

2x-14/5x+2=-1

We move all terms to the left:

2x-14/5x+2-(-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x-14/5x+3=0

We multiply all the terms by the denominator


2x*5x+3*5x-14=0

Wy multiply elements

10x^2+15x-14=0

a = 10; b = 15; c = -14;
Δ = b2-4ac
Δ = 152-4·10·(-14)
Δ = 785
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{785}}{2*10}=\frac{-15-\sqrt{785}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{785}}{2*10}=\frac{-15+\sqrt{785}}{20}
$