5x-3/2x+4=1

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

5x-3/2x+4=1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x-3/2x+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2+6x-3=0

a = 10; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·10·(-3)
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{-(6)-2\sqrt{39}}{2*10}=\frac{-6-2\sqrt{39}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*10}=\frac{-6+2\sqrt{39}}{20}
$