1/2(16x+16)-18=-1/4(24x-28)

Solution for 1/2(16x+16)-18=-1/4(24x-28) equation:

1/2(16x+16)-18=-1/4(24x-28)

We move all terms to the left:

1/2(16x+16)-18-(-1/4(24x-28))=0


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

x∈R



Domain of the equation: 4(24x-28))!=0

x∈R


We calculate fractions


(4x2/(2(16x+16)*4(24x-28)))+(-(-2x1)/(2(16x+16)*4(24x-28)))-18=0


We calculate terms in parentheses: +(4x2/(2(16x+16)*4(24x-28))), so:

4x2/(2(16x+16)*4(24x-28))

We multiply all the terms by the denominator


4x2

We add all the numbers together, and all the variables

4x^2

Back to the equation:

+(4x^2)



We calculate terms in parentheses: +(-(-2x1)/(2(16x+16)*4(24x-28))), so:

-(-2x1)/(2(16x+16)*4(24x-28))

We add all the numbers together, and all the variables

-(-2x)/(2(16x+16)*4(24x-28))

We multiply all the terms by the denominator


-(-2x)

We get rid of parentheses

2x

Back to the equation:

+(2x)


a = 4; b = 2; c = -18;
Δ = b2-4ac
Δ = 22-4·4·(-18)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*4}=\frac{-2-2\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*4}=\frac{-2+2\sqrt{73}}{8}
$