Question 691072
{{{sqrt(3x^2) + 10x - 5 = 0 }}}
Add 5 and subtract 10x from both sides
{{{sqrt(3x^2) = -10x + 5 }}}
Square both sides
{{{(sqrt(3x^2))^2}}} = {{{(-10x+5)^2}}}
FOIL the right side
3x^2 = 100x^2 - 50x - 50x + 25
0 = 100x^2 - 3x^2 - 100x + 25
A quadratic equation
97x^2 - 100x + 25 = 0
Use the quadratic formula to solve this a=97;b=-100;c=25
{{{x = (-(-100) +- sqrt(-100^2-4*97*25 ))/(2*97) }}}
{{{x = (100 +- sqrt(10000-9700 ))/194 }}}
{{{x = (100 +- sqrt(300 ))/194 }}}
Two solutions
{{{x = (100 + 17.32)/194 }}}
x = {{{117.32/194}}}
x = .6047
and
{{{x = (100 - 17.32)/194 }}}
x = {{{82.68/194}}}
x = .4262
: 
but only x=.4262 checks out in the original equation:
{{{sqrt(3*.4262^2) + 10(.4262) - 5 = 0 }}}
{{{sqrt(.545) + 4.262 - 5 = 0 }}}
.7382 + 4.262 - 5 = 0
:
so only x = .4262 is the solution