65-21/2x-x=4x+5

Solution for 65-21/2x-x=4x+5 equation:

65-21/2x-x=4x+5

We move all terms to the left:

65-21/2x-x-(4x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-21/2x-(4x+5)+65=0

We get rid of parentheses

-1x-21/2x-4x-5+65=0

We multiply all the terms by the denominator


-1x*2x-4x*2x-5*2x+65*2x-21=0

Wy multiply elements

-2x^2-8x^2-10x+130x-21=0

We add all the numbers together, and all the variables

-10x^2+120x-21=0

a = -10; b = 120; c = -21;
Δ = b2-4ac
Δ = 1202-4·(-10)·(-21)
Δ = 13560
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:

$\sqrt{\Delta}=\sqrt{13560}=\sqrt{4*3390}=\sqrt{4}*\sqrt{3390}=2\sqrt{3390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3390}}{2*-10}=\frac{-120-2\sqrt{3390}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3390}}{2*-10}=\frac{-120+2\sqrt{3390}}{-20}
$