5x*(5x/4+x)=180

Solution for 5x*(5x/4+x)=180 equation:

5x(5x/4+x)=180

We move all terms to the left:

5x(5x/4+x)-(180)=0


Domain of the equation: 4+x)!=0

We move all terms containing x to the left, all other terms to the right

x)!=-4

x!=-4/1

x!=-4

x∈R


We add all the numbers together, and all the variables

5x(+x+5x/4)-180=0

We multiply parentheses

5x^2+25x^2-180=0

We add all the numbers together, and all the variables

30x^2-180=0

a = 30; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·30·(-180)
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{6}}{2*30}=\frac{0-60\sqrt{6}}{60}
=-\frac{60\sqrt{6}}{60}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{6}}{2*30}=\frac{0+60\sqrt{6}}{60}
=\frac{60\sqrt{6}}{60}
=\sqrt{6}
$