6x(2x-7)=37

Solution for 6x(2x-7)=37 equation:

6x(2x-7)=37

We move all terms to the left:

6x(2x-7)-(37)=0

We multiply parentheses

12x^2-42x-37=0

a = 12; b = -42; c = -37;
Δ = b2-4ac
Δ = -422-4·12·(-37)
Δ = 3540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3540}=\sqrt{4*885}=\sqrt{4}*\sqrt{885}=2\sqrt{885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{885}}{2*12}=\frac{42-2\sqrt{885}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{885}}{2*12}=\frac{42+2\sqrt{885}}{24}
$