# Find all real solutions for the following equation: 2x-3sqrt(x)=20 ?

Nov 7, 2017

no solution

#### Explanation:

The given equation is equivalent to:

$2 x - 20 = 3 \sqrt{x}$

The mixed system that solves it will be:

$x \ge 0 \mathmr{and} 2 x - 20 \ge 0 \mathmr{and} {\left(2 x - 20\right)}^{2} = {\left(3 \sqrt{x}\right)}^{2}$

that's

$x \ge 0 \mathmr{and} x \ge 10 \mathmr{and} 4 {x}^{2} - 80 x + 400 = 9 {x}^{2}$

$x \ge 10 \mathmr{and} 5 {x}^{2} + 80 x - 400 = 0$

$x \ge 10 \mathmr{and} {x}^{2} + 16 x - 80 = 0$

$x \ge 10 \mathmr{and} x = - 8 \pm \sqrt{64 + 80}$

$x \ge 10 \mathmr{and} x = - 8 \pm \sqrt{144}$

$x \ge 10 \mathmr{and} x = - 8 \pm 12$

that has no solution