-x+3=5/2x-4

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

-x+3=5/2x-4

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2+8x+6x-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}
$