-10x+4/5x+2=16

Solution for -10x+4/5x+2=16 equation:

-10x+4/5x+2=16

We move all terms to the left:

-10x+4/5x+2-(16)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+4/5x-14=0

We multiply all the terms by the denominator


-10x*5x-14*5x+4=0

Wy multiply elements

-50x^2-70x+4=0

a = -50; b = -70; c = +4;
Δ = b2-4ac
Δ = -702-4·(-50)·4
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{57}}{2*-50}=\frac{70-10\sqrt{57}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{57}}{2*-50}=\frac{70+10\sqrt{57}}{-100}
$