37x+x2=1764

Solution for 37x+x2=1764 equation:

37x+x2=1764

We move all terms to the left:

37x+x2-(1764)=0

We add all the numbers together, and all the variables

x^2+37x-1764=0

a = 1; b = 37; c = -1764;
Δ = b2-4ac
Δ = 372-4·1·(-1764)
Δ = 8425
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:

$\sqrt{\Delta}=\sqrt{8425}=\sqrt{25*337}=\sqrt{25}*\sqrt{337}=5\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-5\sqrt{337}}{2*1}=\frac{-37-5\sqrt{337}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+5\sqrt{337}}{2*1}=\frac{-37+5\sqrt{337}}{2}
$