150=8x+7/x

Solution for 150=8x+7/x equation:

150=8x+7/x

We move all terms to the left:

150-(8x+7/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+8x+7/x)+150=0

We get rid of parentheses

-8x-7/x+150=0

We multiply all the terms by the denominator


-8x*x+150*x-7=0

We add all the numbers together, and all the variables

150x-8x*x-7=0

Wy multiply elements

-8x^2+150x-7=0

a = -8; b = 150; c = -7;
Δ = b2-4ac
Δ = 1502-4·(-8)·(-7)
Δ = 22276
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:

$\sqrt{\Delta}=\sqrt{22276}=\sqrt{4*5569}=\sqrt{4}*\sqrt{5569}=2\sqrt{5569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5569}}{2*-8}=\frac{-150-2\sqrt{5569}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5569}}{2*-8}=\frac{-150+2\sqrt{5569}}{-16}
$