25/5x-7x=12

Solution for 25/5x-7x=12 equation:

25/5x-7x=12

We move all terms to the left:

25/5x-7x-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+25/5x-12=0

We multiply all the terms by the denominator


-7x*5x-12*5x+25=0

Wy multiply elements

-35x^2-60x+25=0

a = -35; b = -60; c = +25;
Δ = b2-4ac
Δ = -602-4·(-35)·25
Δ = 7100
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:

$\sqrt{\Delta}=\sqrt{7100}=\sqrt{100*71}=\sqrt{100}*\sqrt{71}=10\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{71}}{2*-35}=\frac{60-10\sqrt{71}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{71}}{2*-35}=\frac{60+10\sqrt{71}}{-70}
$