5-3x=1/2x-7

Solution for 5-3x=1/2x-7 equation:

5-3x=1/2x-7

We move all terms to the left:

5-3x-(1/2x-7)=0


Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

-3x-1/2x+7+5=0

We multiply all the terms by the denominator


-3x*2x+7*2x+5*2x-1=0

Wy multiply elements

-6x^2+14x+10x-1=0

We add all the numbers together, and all the variables

-6x^2+24x-1=0

a = -6; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-6)·(-1)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{138}}{2*-6}=\frac{-24-2\sqrt{138}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{138}}{2*-6}=\frac{-24+2\sqrt{138}}{-12}
$