31/2x+245=260x+4

Solution for 31/2x+245=260x+4 equation:

31/2x+245=260x+4

We move all terms to the left:

31/2x+245-(260x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

31/2x-260x-4+245=0

We multiply all the terms by the denominator


-260x*2x-4*2x+245*2x+31=0

Wy multiply elements

-520x^2-8x+490x+31=0

We add all the numbers together, and all the variables

-520x^2+482x+31=0

a = -520; b = 482; c = +31;
Δ = b2-4ac
Δ = 4822-4·(-520)·31
Δ = 296804
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:

$\sqrt{\Delta}=\sqrt{296804}=\sqrt{4*74201}=\sqrt{4}*\sqrt{74201}=2\sqrt{74201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(482)-2\sqrt{74201}}{2*-520}=\frac{-482-2\sqrt{74201}}{-1040}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(482)+2\sqrt{74201}}{2*-520}=\frac{-482+2\sqrt{74201}}{-1040}
$