3/10*x=9

Solution for 3/10*x=9 equation:

3/10*x=9

We move all terms to the left:

3/10*x-(9)=0


Domain of the equation: 10*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-9*10*x+3=0

Wy multiply elements

-90x*x+3=0

Wy multiply elements

-90x^2+3=0

a = -90; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-90)·3
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*-90}=\frac{0-6\sqrt{30}}{-180}
=-\frac{6\sqrt{30}}{-180}
=-\frac{\sqrt{30}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*-90}=\frac{0+6\sqrt{30}}{-180}
=\frac{6\sqrt{30}}{-180}
=\frac{\sqrt{30}}{-30}
$