8x(x+4)+3(x-3)=0

Solution for 8x(x+4)+3(x-3)=0 equation:

8x(x+4)+3(x-3)=0

We multiply parentheses

8x^2+32x+3x-9=0

We add all the numbers together, and all the variables

8x^2+35x-9=0

a = 8; b = 35; c = -9;
Δ = b2-4ac
Δ = 352-4·8·(-9)
Δ = 1513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1513}}{2*8}=\frac{-35-\sqrt{1513}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1513}}{2*8}=\frac{-35+\sqrt{1513}}{16}
$