(90-7x^2)/x=-112

Solution for (90-7x^2)/x=-112 equation:

(90-7x^2)/x=-112

We move all terms to the left:

(90-7x^2)/x-(-112)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(90-7x^2)/x+112=0

We multiply all the terms by the denominator


(90-7x^2)+112*x=0

We add all the numbers together, and all the variables

(90-7x^2)+112x=0

We get rid of parentheses

-7x^2+112x+90=0

a = -7; b = 112; c = +90;
Δ = b2-4ac
Δ = 1122-4·(-7)·90
Δ = 15064
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:

$\sqrt{\Delta}=\sqrt{15064}=\sqrt{4*3766}=\sqrt{4}*\sqrt{3766}=2\sqrt{3766}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-2\sqrt{3766}}{2*-7}=\frac{-112-2\sqrt{3766}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+2\sqrt{3766}}{2*-7}=\frac{-112+2\sqrt{3766}}{-14}
$