8x+9x^2=52

Solution for 8x+9x^2=52 equation:

8x+9x^2=52

We move all terms to the left:

8x+9x^2-(52)=0

a = 9; b = 8; c = -52;
Δ = b2-4ac
Δ = 82-4·9·(-52)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-44}{2*9}=\frac{-52}{18}
=-2+8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+44}{2*9}=\frac{36}{18}
=2
$