1/2(x)=10x+4

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

1/2(x)=10x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-10x-4=0

We multiply all the terms by the denominator


-10x*2x-4*2x+1=0

Wy multiply elements

-20x^2-8x+1=0

a = -20; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-20)·1
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-20}=\frac{-4}{-40}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-20}=\frac{20}{-40}
=-1/2
$