8x-3=15/10x

Solution for 8x-3=15/10x equation:

8x-3=15/10x

We move all terms to the left:

8x-3-(15/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+15/10x)-3=0

We get rid of parentheses

8x-15/10x-3=0

We multiply all the terms by the denominator


8x*10x-3*10x-15=0

Wy multiply elements

80x^2-30x-15=0

a = 80; b = -30; c = -15;
Δ = b2-4ac
Δ = -302-4·80·(-15)
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{57}}{2*80}=\frac{30-10\sqrt{57}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{57}}{2*80}=\frac{30+10\sqrt{57}}{160}
$