4x=(-6x-10)^(1/2)

Solution for 4x=(-6x-10)^(1/2) equation:

4x=(-6x-10)^(1/2)

We move all terms to the left:

4x-((-6x-10)^(1/2))=0

We add all the numbers together, and all the variables

4x-((-6x-10)^(+1/2))=0

We multiply all the terms by the denominator


4x*2))-((-6x+1-10)^(=0

We add all the numbers together, and all the variables

4x*2))-((-6x-9)^(=0

We add all the numbers together, and all the variables

-6x+4x*2))-((=0

Wy multiply elements

8x^2-6x=0

a = 8; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·8·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*8}=\frac{12}{16}
=3/4
$