3/10x=37x+14=

Solution for 3/10x=37x+14= equation:

3/10x=37x+14=

We move all terms to the left:

3/10x-(37x+14)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

3/10x-37x-14=0

We multiply all the terms by the denominator


-37x*10x-14*10x+3=0

Wy multiply elements

-370x^2-140x+3=0

a = -370; b = -140; c = +3;
Δ = b2-4ac
Δ = -1402-4·(-370)·3
Δ = 24040
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:

$\sqrt{\Delta}=\sqrt{24040}=\sqrt{4*6010}=\sqrt{4}*\sqrt{6010}=2\sqrt{6010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{6010}}{2*-370}=\frac{140-2\sqrt{6010}}{-740}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{6010}}{2*-370}=\frac{140+2\sqrt{6010}}{-740}
$