10x-7/19x=62

Solution for 10x-7/19x=62 equation:

10x-7/19x=62

We move all terms to the left:

10x-7/19x-(62)=0


Domain of the equation: 19x!=0

x!=0/19

x!=0

x∈R


We multiply all the terms by the denominator


10x*19x-62*19x-7=0

Wy multiply elements

190x^2-1178x-7=0

a = 190; b = -1178; c = -7;
Δ = b2-4ac
Δ = -11782-4·190·(-7)
Δ = 1393004
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:

$\sqrt{\Delta}=\sqrt{1393004}=\sqrt{4*348251}=\sqrt{4}*\sqrt{348251}=2\sqrt{348251}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1178)-2\sqrt{348251}}{2*190}=\frac{1178-2\sqrt{348251}}{380}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1178)+2\sqrt{348251}}{2*190}=\frac{1178+2\sqrt{348251}}{380}
$