37x^2+29x-31=29x-6

Solution for 37x^2+29x-31=29x-6 equation:

37x^2+29x-31=29x-6

We move all terms to the left:

37x^2+29x-31-(29x-6)=0

We get rid of parentheses

37x^2+29x-29x+6-31=0

We add all the numbers together, and all the variables

37x^2-25=0

a = 37; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·37·(-25)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{37}}{2*37}=\frac{0-10\sqrt{37}}{74}
=-\frac{10\sqrt{37}}{74}
=-\frac{5\sqrt{37}}{37}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{37}}{2*37}=\frac{0+10\sqrt{37}}{74}
=\frac{10\sqrt{37}}{74}
=\frac{5\sqrt{37}}{37}
$