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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

40x^2+39x-585=0

a = 40; b = 39; c = -585;
Δ = b2-4ac
Δ = 392-4·40·(-585)
Δ = 95121
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:

$\sqrt{\Delta}=\sqrt{95121}=\sqrt{9*10569}=\sqrt{9}*\sqrt{10569}=3\sqrt{10569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{10569}}{2*40}=\frac{-39-3\sqrt{10569}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{10569}}{2*40}=\frac{-39+3\sqrt{10569}}{80}
$