7/5x+x=96

Solution for 7/5x+x=96 equation:

7/5x+x=96

We move all terms to the left:

7/5x+x-(96)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+7/5x-96=0

We multiply all the terms by the denominator


x*5x-96*5x+7=0

Wy multiply elements

5x^2-480x+7=0

a = 5; b = -480; c = +7;
Δ = b2-4ac
Δ = -4802-4·5·7
Δ = 230260
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:

$\sqrt{\Delta}=\sqrt{230260}=\sqrt{4*57565}=\sqrt{4}*\sqrt{57565}=2\sqrt{57565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{57565}}{2*5}=\frac{480-2\sqrt{57565}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{57565}}{2*5}=\frac{480+2\sqrt{57565}}{10}
$