10x+1/2(8x)=38.50

Solution for 10x+1/2(8x)=38.50 equation:

10x+1/2(8x)=38.50

We move all terms to the left:

10x+1/2(8x)-(38.50)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We add all the numbers together, and all the variables

10x+1/28x-(38.5)=0

We add all the numbers together, and all the variables

10x+1/28x-38.5=0

We multiply all the terms by the denominator


10x*28x-(38.5)*28x+1=0

We multiply parentheses

10x*28x-1078x+1=0

Wy multiply elements

280x^2-1078x+1=0

a = 280; b = -1078; c = +1;
Δ = b2-4ac
Δ = -10782-4·280·1
Δ = 1160964
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:

$\sqrt{\Delta}=\sqrt{1160964}=\sqrt{36*32249}=\sqrt{36}*\sqrt{32249}=6\sqrt{32249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1078)-6\sqrt{32249}}{2*280}=\frac{1078-6\sqrt{32249}}{560}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1078)+6\sqrt{32249}}{2*280}=\frac{1078+6\sqrt{32249}}{560}
$