x+7x2-3=37

Solution for x+7x2-3=37 equation:

x+7x^2-3=37

We move all terms to the left:

x+7x^2-3-(37)=0

We add all the numbers together, and all the variables

7x^2+x-40=0

a = 7; b = 1; c = -40;
Δ = b2-4ac
Δ = 12-4·7·(-40)
Δ = 1121
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{-(1)-\sqrt{1121}}{2*7}=\frac{-1-\sqrt{1121}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1121}}{2*7}=\frac{-1+\sqrt{1121}}{14}
$