-7x+5/7x+2=-18

Solution for -7x+5/7x+2=-18 equation:

-7x+5/7x+2=-18

We move all terms to the left:

-7x+5/7x+2-(-18)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+5/7x+20=0

We multiply all the terms by the denominator


-7x*7x+20*7x+5=0

Wy multiply elements

-49x^2+140x+5=0

a = -49; b = 140; c = +5;
Δ = b2-4ac
Δ = 1402-4·(-49)·5
Δ = 20580
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:

$\sqrt{\Delta}=\sqrt{20580}=\sqrt{196*105}=\sqrt{196}*\sqrt{105}=14\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-14\sqrt{105}}{2*-49}=\frac{-140-14\sqrt{105}}{-98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+14\sqrt{105}}{2*-49}=\frac{-140+14\sqrt{105}}{-98}
$