10x+8/7x=14

Solution for 10x+8/7x=14 equation:

10x+8/7x=14

We move all terms to the left:

10x+8/7x-(14)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


10x*7x-14*7x+8=0

Wy multiply elements

70x^2-98x+8=0

a = 70; b = -98; c = +8;
Δ = b2-4ac
Δ = -982-4·70·8
Δ = 7364
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:

$\sqrt{\Delta}=\sqrt{7364}=\sqrt{4*1841}=\sqrt{4}*\sqrt{1841}=2\sqrt{1841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{1841}}{2*70}=\frac{98-2\sqrt{1841}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{1841}}{2*70}=\frac{98+2\sqrt{1841}}{140}
$