9x^2=35x+4

Solution for 9x^2=35x+4 equation:

9x^2=35x+4

We move all terms to the left:

9x^2-(35x+4)=0

We get rid of parentheses

9x^2-35x-4=0

a = 9; b = -35; c = -4;
Δ = b2-4ac
Δ = -352-4·9·(-4)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-37}{2*9}=\frac{-2}{18}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+37}{2*9}=\frac{72}{18}
=4
$