63=x+x-2+1/2x

Solution for 63=x+x-2+1/2x equation:

63=x+x-2+1/2x

We move all terms to the left:

63-(x+x-2+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(2x+1/2x-2)+63=0

We get rid of parentheses

-2x-1/2x+2+63=0

We multiply all the terms by the denominator


-2x*2x+2*2x+63*2x-1=0

Wy multiply elements

-4x^2+4x+126x-1=0

We add all the numbers together, and all the variables

-4x^2+130x-1=0

a = -4; b = 130; c = -1;
Δ = b2-4ac
Δ = 1302-4·(-4)·(-1)
Δ = 16884
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:

$\sqrt{\Delta}=\sqrt{16884}=\sqrt{36*469}=\sqrt{36}*\sqrt{469}=6\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-6\sqrt{469}}{2*-4}=\frac{-130-6\sqrt{469}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+6\sqrt{469}}{2*-4}=\frac{-130+6\sqrt{469}}{-8}
$