3x^2-37x=5x-20

Solution for 3x^2-37x=5x-20 equation:

3x^2-37x=5x-20

We move all terms to the left:

3x^2-37x-(5x-20)=0

We get rid of parentheses

3x^2-37x-5x+20=0

We add all the numbers together, and all the variables

3x^2-42x+20=0

a = 3; b = -42; c = +20;
Δ = b2-4ac
Δ = -422-4·3·20
Δ = 1524
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:

$\sqrt{\Delta}=\sqrt{1524}=\sqrt{4*381}=\sqrt{4}*\sqrt{381}=2\sqrt{381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{381}}{2*3}=\frac{42-2\sqrt{381}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{381}}{2*3}=\frac{42+2\sqrt{381}}{6}
$