a(a+3/5)=375

Solution for a(a+3/5)=375 equation:

a(a+3/5)=375

We move all terms to the left:

a(a+3/5)-(375)=0

We add all the numbers together, and all the variables

a(+a+3/5)-375=0

We multiply parentheses

a^2+3a^2-375=0

We add all the numbers together, and all the variables

4a^2-375=0

a = 4; b = 0; c = -375;
Δ = b2-4ac
Δ = 02-4·4·(-375)
Δ = 6000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*4}=\frac{0-20\sqrt{15}}{8}
=-\frac{20\sqrt{15}}{8}
=-\frac{5\sqrt{15}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*4}=\frac{0+20\sqrt{15}}{8}
=\frac{20\sqrt{15}}{8}
=\frac{5\sqrt{15}}{2}
$