x-19/25x=12

Solution for x-19/25x=12 equation:

x-19/25x=12

We move all terms to the left:

x-19/25x-(12)=0


Domain of the equation: 25x!=0

x!=0/25

x!=0

x∈R


We multiply all the terms by the denominator


x*25x-12*25x-19=0

Wy multiply elements

25x^2-300x-19=0

a = 25; b = -300; c = -19;
Δ = b2-4ac
Δ = -3002-4·25·(-19)
Δ = 91900
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:

$\sqrt{\Delta}=\sqrt{91900}=\sqrt{100*919}=\sqrt{100}*\sqrt{919}=10\sqrt{919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-10\sqrt{919}}{2*25}=\frac{300-10\sqrt{919}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+10\sqrt{919}}{2*25}=\frac{300+10\sqrt{919}}{50}
$