x-11/10x=15

Solution for x-11/10x=15 equation:

x-11/10x=15

We move all terms to the left:

x-11/10x-(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-11=0

Wy multiply elements

10x^2-150x-11=0

a = 10; b = -150; c = -11;
Δ = b2-4ac
Δ = -1502-4·10·(-11)
Δ = 22940
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:

$\sqrt{\Delta}=\sqrt{22940}=\sqrt{4*5735}=\sqrt{4}*\sqrt{5735}=2\sqrt{5735}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5735}}{2*10}=\frac{150-2\sqrt{5735}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5735}}{2*10}=\frac{150+2\sqrt{5735}}{20}
$