78=1/2(x)(1x)+24(x)

Solution for 78=1/2(x)(1x)+24(x) equation:

78=1/2(x)(1x)+24(x)

We move all terms to the left:

78-(1/2(x)(1x)+24(x))=0


Domain of the equation: 2x1x+24x)!=0

x∈R


We add all the numbers together, and all the variables

-(+24x+1/2x1x)+78=0

We get rid of parentheses

-24x-1/2x1x+78=0

We multiply all the terms by the denominator


-24x*2x1x+78*2x1x-1=0

Wy multiply elements

-48x^2+156x-1=0

a = -48; b = 156; c = -1;
Δ = b2-4ac
Δ = 1562-4·(-48)·(-1)
Δ = 24144
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:

$\sqrt{\Delta}=\sqrt{24144}=\sqrt{16*1509}=\sqrt{16}*\sqrt{1509}=4\sqrt{1509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-4\sqrt{1509}}{2*-48}=\frac{-156-4\sqrt{1509}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+4\sqrt{1509}}{2*-48}=\frac{-156+4\sqrt{1509}}{-96}
$