8x+10=1/2(5x)

Solution for 8x+10=1/2(5x) equation:

8x+10=1/2(5x)

We move all terms to the left:

8x+10-(1/2(5x))=0


Domain of the equation: 25x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+1/25x)+10=0

We get rid of parentheses

8x-1/25x+10=0

We multiply all the terms by the denominator


8x*25x+10*25x-1=0

Wy multiply elements

200x^2+250x-1=0

a = 200; b = 250; c = -1;
Δ = b2-4ac
Δ = 2502-4·200·(-1)
Δ = 63300
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:

$\sqrt{\Delta}=\sqrt{63300}=\sqrt{100*633}=\sqrt{100}*\sqrt{633}=10\sqrt{633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{633}}{2*200}=\frac{-250-10\sqrt{633}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{633}}{2*200}=\frac{-250+10\sqrt{633}}{400}
$