(9x-8)(x+6)=-4

Solution for (9x-8)(x+6)=-4 equation:

(9x-8)(x+6)=-4

We move all terms to the left:

(9x-8)(x+6)-(-4)=0

We add all the numbers together, and all the variables

(9x-8)(x+6)+4=0

We multiply parentheses ..

(+9x^2+54x-8x-48)+4=0

We get rid of parentheses

9x^2+54x-8x-48+4=0

We add all the numbers together, and all the variables

9x^2+46x-44=0

a = 9; b = 46; c = -44;
Δ = b2-4ac
Δ = 462-4·9·(-44)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-10\sqrt{37}}{2*9}=\frac{-46-10\sqrt{37}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+10\sqrt{37}}{2*9}=\frac{-46+10\sqrt{37}}{18}
$