3/7x=10+16x

Solution for 3/7x=10+16x equation:

3/7x=10+16x

We move all terms to the left:

3/7x-(10+16x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

3/7x-(16x+10)=0

We get rid of parentheses

3/7x-16x-10=0

We multiply all the terms by the denominator


-16x*7x-10*7x+3=0

Wy multiply elements

-112x^2-70x+3=0

a = -112; b = -70; c = +3;
Δ = b2-4ac
Δ = -702-4·(-112)·3
Δ = 6244
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:

$\sqrt{\Delta}=\sqrt{6244}=\sqrt{4*1561}=\sqrt{4}*\sqrt{1561}=2\sqrt{1561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1561}}{2*-112}=\frac{70-2\sqrt{1561}}{-224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1561}}{2*-112}=\frac{70+2\sqrt{1561}}{-224}
$