10a(a-3)=15

Solution for 10a(a-3)=15 equation:

10a(a-3)=15

We move all terms to the left:

10a(a-3)-(15)=0

We multiply parentheses

10a^2-30a-15=0

a = 10; b = -30; c = -15;
Δ = b2-4ac
Δ = -302-4·10·(-15)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{15}}{2*10}=\frac{30-10\sqrt{15}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{15}}{2*10}=\frac{30+10\sqrt{15}}{20}
$