3x^2+4x-37=0

Solution for 3x^2+4x-37=0 equation:

3x^2+4x-37=0

a = 3; b = 4; c = -37;
Δ = b2-4ac
Δ = 42-4·3·(-37)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{115}}{2*3}=\frac{-4-2\sqrt{115}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{115}}{2*3}=\frac{-4+2\sqrt{115}}{6}
$