37x2-172x-162=0

Solution for 37x2-172x-162=0 equation:

37x^2-172x-162=0

a = 37; b = -172; c = -162;
Δ = b2-4ac
Δ = -1722-4·37·(-162)
Δ = 53560
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:

$\sqrt{\Delta}=\sqrt{53560}=\sqrt{4*13390}=\sqrt{4}*\sqrt{13390}=2\sqrt{13390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-2\sqrt{13390}}{2*37}=\frac{172-2\sqrt{13390}}{74}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+2\sqrt{13390}}{2*37}=\frac{172+2\sqrt{13390}}{74}
$