35x^2+x=6

Solution for 35x^2+x=6 equation:

35x^2+x=6

We move all terms to the left:

35x^2+x-(6)=0

a = 35; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·35·(-6)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*35}=\frac{-30}{70}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*35}=\frac{28}{70}
=2/5
$