5/2x-4=-x+3

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

5/2x-4=-x+3

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-6x-8x+5=0

We add all the numbers together, and all the variables

2x^2-14x+5=0

a = 2; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·2·5
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*2}=\frac{14-2\sqrt{39}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*2}=\frac{14+2\sqrt{39}}{4}
$