x-9/10x=15

Solution for x-9/10x=15 equation:

x-9/10x=15

We move all terms to the left:

x-9/10x-(15)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-15*10x-9=0

Wy multiply elements

10x^2-150x-9=0

a = 10; b = -150; c = -9;
Δ = b2-4ac
Δ = -1502-4·10·(-9)
Δ = 22860
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:

$\sqrt{\Delta}=\sqrt{22860}=\sqrt{36*635}=\sqrt{36}*\sqrt{635}=6\sqrt{635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-6\sqrt{635}}{2*10}=\frac{150-6\sqrt{635}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+6\sqrt{635}}{2*10}=\frac{150+6\sqrt{635}}{20}
$