4x=38(-1/2)(4x+16)

Solution for 4x=38(-1/2)(4x+16) equation:

4x=38(-1/2)(4x+16)

We move all terms to the left:

4x-(38(-1/2)(4x+16))=0


Domain of the equation: 2)(4x+16))!=0

x∈R


We multiply parentheses ..

-(38(-4x^2-1/2*16))+4x=0

We multiply all the terms by the denominator


-(38(-4x^2-1+4x*2*16))=0


We calculate terms in parentheses: -(38(-4x^2-1+4x*2*16)), so:

38(-4x^2-1+4x*2*16)

We multiply parentheses

-152x^2+4864x-38

Back to the equation:

-(-152x^2+4864x-38)


We get rid of parentheses

152x^2-4864x+38=0

a = 152; b = -4864; c = +38;
Δ = b2-4ac
Δ = -48642-4·152·38
Δ = 23635392
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:

$\sqrt{\Delta}=\sqrt{23635392}=\sqrt{23104*1023}=\sqrt{23104}*\sqrt{1023}=152\sqrt{1023}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4864)-152\sqrt{1023}}{2*152}=\frac{4864-152\sqrt{1023}}{304}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4864)+152\sqrt{1023}}{2*152}=\frac{4864+152\sqrt{1023}}{304}
$