-21/7x-5x=24

Solution for -21/7x-5x=24 equation:

-21/7x-5x=24

We move all terms to the left:

-21/7x-5x-(24)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-5x-21/7x-24=0

We multiply all the terms by the denominator


-5x*7x-24*7x-21=0

Wy multiply elements

-35x^2-168x-21=0

a = -35; b = -168; c = -21;
Δ = b2-4ac
Δ = -1682-4·(-35)·(-21)
Δ = 25284
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:

$\sqrt{\Delta}=\sqrt{25284}=\sqrt{196*129}=\sqrt{196}*\sqrt{129}=14\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-14\sqrt{129}}{2*-35}=\frac{168-14\sqrt{129}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+14\sqrt{129}}{2*-35}=\frac{168+14\sqrt{129}}{-70}
$