0.5x(8x+1)=1.5-(2-4x)

Solution for 0.5x(8x+1)=1.5-(2-4x) equation:

0.5x(8x+1)=1.5-(2-4x)

We move all terms to the left:

0.5x(8x+1)-(1.5-(2-4x))=0

We add all the numbers together, and all the variables

0.5x(8x+1)-(1.5-(-4x+2))=0

We multiply parentheses

0x^2+0x-(1.5-(-4x+2))=0


We calculate terms in parentheses: -(1.5-(-4x+2)), so:

1.5-(-4x+2)

determiningTheFunctionDomain
-(-4x+2)+1.5

We get rid of parentheses

4x-2+1.5

We add all the numbers together, and all the variables

4x-0.5

Back to the equation:

-(4x-0.5)


We add all the numbers together, and all the variables

x^2+x-(4x-0.5)=0

We get rid of parentheses

x^2+x-4x+0.5=0

We add all the numbers together, and all the variables

x^2-3x+0.5=0

a = 1; b = -3; c = +0.5;
Δ = b2-4ac
Δ = -32-4·1·0.5
Δ = 7
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{7}}{2*1}=\frac{3-\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{7}}{2*1}=\frac{3+\sqrt{7}}{2}
$