3x(6x-5)=7

Solution for 3x(6x-5)=7 equation:

3x(6x-5)=7

We move all terms to the left:

3x(6x-5)-(7)=0

We multiply parentheses

18x^2-15x-7=0

a = 18; b = -15; c = -7;
Δ = b2-4ac
Δ = -152-4·18·(-7)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-27}{2*18}=\frac{-12}{36}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+27}{2*18}=\frac{42}{36}
=1+1/6
$