9x^2-19=4x

Solution for 9x^2-19=4x equation:

9x^2-19=4x

We move all terms to the left:

9x^2-19-(4x)=0

a = 9; b = -4; c = -19;
Δ = b2-4ac
Δ = -42-4·9·(-19)
Δ = 700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10\sqrt{7}}{2*9}=\frac{4-10\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10\sqrt{7}}{2*9}=\frac{4+10\sqrt{7}}{18}
$