1/2(10x)+4=3x+8

Solution for 1/2(10x)+4=3x+8 equation:

1/2(10x)+4=3x+8

We move all terms to the left:

1/2(10x)+4-(3x+8)=0


Domain of the equation: 210x!=0

x!=0/210

x!=0

x∈R


We get rid of parentheses

1/210x-3x-8+4=0

We multiply all the terms by the denominator


-3x*210x-8*210x+4*210x+1=0

Wy multiply elements

-630x^2-1680x+840x+1=0

We add all the numbers together, and all the variables

-630x^2-840x+1=0

a = -630; b = -840; c = +1;
Δ = b2-4ac
Δ = -8402-4·(-630)·1
Δ = 708120
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:

$\sqrt{\Delta}=\sqrt{708120}=\sqrt{36*19670}=\sqrt{36}*\sqrt{19670}=6\sqrt{19670}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-6\sqrt{19670}}{2*-630}=\frac{840-6\sqrt{19670}}{-1260}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+6\sqrt{19670}}{2*-630}=\frac{840+6\sqrt{19670}}{-1260}
$