9x2+5x=4

Solution for 9x2+5x=4 equation:

9x^2+5x=4

We move all terms to the left:

9x^2+5x-(4)=0

a = 9; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·9·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*9}=\frac{8}{18}
=4/9
$