4x-12/x=-10

Solution for 4x-12/x=-10 equation:

4x-12/x=-10

We move all terms to the left:

4x-12/x-(-10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-12/x+10=0

We multiply all the terms by the denominator


4x*x+10*x-12=0

We add all the numbers together, and all the variables

10x+4x*x-12=0

Wy multiply elements

4x^2+10x-12=0

a = 4; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·4·(-12)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{73}}{2*4}=\frac{-10-2\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{73}}{2*4}=\frac{-10+2\sqrt{73}}{8}
$