5x-3=4-1/2x

Solution for 5x-3=4-1/2x equation:

5x-3=4-1/2x

We move all terms to the left:

5x-3-(4-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(-1/2x+4)-3=0

We get rid of parentheses

5x+1/2x-4-3=0

We multiply all the terms by the denominator


5x*2x-4*2x-3*2x+1=0

Wy multiply elements

10x^2-8x-6x+1=0

We add all the numbers together, and all the variables

10x^2-14x+1=0

a = 10; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·10·1
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*10}=\frac{14-2\sqrt{39}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*10}=\frac{14+2\sqrt{39}}{20}
$