35x^2=13x+4

Solution for 35x^2=13x+4 equation:

35x^2=13x+4

We move all terms to the left:

35x^2-(13x+4)=0

We get rid of parentheses

35x^2-13x-4=0

a = 35; b = -13; c = -4;
Δ = b2-4ac
Δ = -132-4·35·(-4)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-27}{2*35}=\frac{-14}{70}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+27}{2*35}=\frac{40}{70}
=4/7
$