37x-5-7x^2=0

Solution for 37x-5-7x^2=0 equation:

37x-5-7x^2=0

a = -7; b = 37; c = -5;
Δ = b2-4ac
Δ = 372-4·(-7)·(-5)
Δ = 1229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-\sqrt{1229}}{2*-7}=\frac{-37-\sqrt{1229}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{1229}}{2*-7}=\frac{-37+\sqrt{1229}}{-14}
$