35q^2-13=5027

Solution for 35q^2-13=5027 equation:

35q^2-13=5027

We move all terms to the left:

35q^2-13-(5027)=0

We add all the numbers together, and all the variables

35q^2-5040=0

a = 35; b = 0; c = -5040;
Δ = b2-4ac
Δ = 02-4·35·(-5040)
Δ = 705600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{705600}=840$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-840}{2*35}=\frac{-840}{70}
=-12
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+840}{2*35}=\frac{840}{70}
=12
$