5x-3/10x=3

Solution for 5x-3/10x=3 equation:

5x-3/10x=3

We move all terms to the left:

5x-3/10x-(3)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


5x*10x-3*10x-3=0

Wy multiply elements

50x^2-30x-3=0

a = 50; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·50·(-3)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{15}}{2*50}=\frac{30-10\sqrt{15}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{15}}{2*50}=\frac{30+10\sqrt{15}}{100}
$