6(3a-2)5a=57

Solution for 6(3a-2)5a=57 equation:

6(3a-2)5a=57

We move all terms to the left:

6(3a-2)5a-(57)=0

We multiply parentheses

90a^2-60a-57=0

a = 90; b = -60; c = -57;
Δ = b2-4ac
Δ = -602-4·90·(-57)
Δ = 24120
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:

$\sqrt{\Delta}=\sqrt{24120}=\sqrt{36*670}=\sqrt{36}*\sqrt{670}=6\sqrt{670}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{670}}{2*90}=\frac{60-6\sqrt{670}}{180}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{670}}{2*90}=\frac{60+6\sqrt{670}}{180}
$