1/295x+12)=2x-3

Solution for 1/295x+12)=2x-3 equation:

1/295x+12)=2x-3

We move all terms to the left:

1/295x+12)-(2x-3)=0


Domain of the equation: 295x!=0

x!=0/295

x!=0

x∈R


We add all the numbers together, and all the variables

1/295x+12)-(2x=0

We multiply all the terms by the denominator


-2x*295x+1+12=0

We add all the numbers together, and all the variables

-2x*295x+13=0

Wy multiply elements

-590x^2+13=0

a = -590; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-590)·13
Δ = 30680
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:

$\sqrt{\Delta}=\sqrt{30680}=\sqrt{4*7670}=\sqrt{4}*\sqrt{7670}=2\sqrt{7670}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7670}}{2*-590}=\frac{0-2\sqrt{7670}}{-1180}
=-\frac{2\sqrt{7670}}{-1180}
=-\frac{\sqrt{7670}}{-590}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7670}}{2*-590}=\frac{0+2\sqrt{7670}}{-1180}
=\frac{2\sqrt{7670}}{-1180}
=\frac{\sqrt{7670}}{-590}
$