x+7/10x=16

Solution for x+7/10x=16 equation:

x+7/10x=16

We move all terms to the left:

x+7/10x-(16)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-16*10x+7=0

Wy multiply elements

10x^2-160x+7=0

a = 10; b = -160; c = +7;
Δ = b2-4ac
Δ = -1602-4·10·7
Δ = 25320
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:

$\sqrt{\Delta}=\sqrt{25320}=\sqrt{4*6330}=\sqrt{4}*\sqrt{6330}=2\sqrt{6330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-2\sqrt{6330}}{2*10}=\frac{160-2\sqrt{6330}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+2\sqrt{6330}}{2*10}=\frac{160+2\sqrt{6330}}{20}
$