(8x+3)(5x+3)-40x=594

Solution for (8x+3)(5x+3)-40x=594 equation:

(8x+3)(5x+3)-40x=594

We move all terms to the left:

(8x+3)(5x+3)-40x-(594)=0

We add all the numbers together, and all the variables

-40x+(8x+3)(5x+3)-594=0

We multiply parentheses ..

(+40x^2+24x+15x+9)-40x-594=0

We get rid of parentheses

40x^2+24x+15x-40x+9-594=0

We add all the numbers together, and all the variables

40x^2-1x-585=0

a = 40; b = -1; c = -585;
Δ = b2-4ac
Δ = -12-4·40·(-585)
Δ = 93601
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{-(-1)-\sqrt{93601}}{2*40}=\frac{1-\sqrt{93601}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{93601}}{2*40}=\frac{1+\sqrt{93601}}{80}
$