15a(3a+4)=6

Solution for 15a(3a+4)=6 equation:

15a(3a+4)=6

We move all terms to the left:

15a(3a+4)-(6)=0

We multiply parentheses

45a^2+60a-6=0

a = 45; b = 60; c = -6;
Δ = b2-4ac
Δ = 602-4·45·(-6)
Δ = 4680
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:

$\sqrt{\Delta}=\sqrt{4680}=\sqrt{36*130}=\sqrt{36}*\sqrt{130}=6\sqrt{130}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-6\sqrt{130}}{2*45}=\frac{-60-6\sqrt{130}}{90}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+6\sqrt{130}}{2*45}=\frac{-60+6\sqrt{130}}{90}
$