(4x+6)(4x-5)=73

Solution for (4x+6)(4x-5)=73 equation:

(4x+6)(4x-5)=73

We move all terms to the left:

(4x+6)(4x-5)-(73)=0

We multiply parentheses ..

(+16x^2-20x+24x-30)-73=0

We get rid of parentheses

16x^2-20x+24x-30-73=0

We add all the numbers together, and all the variables

16x^2+4x-103=0

a = 16; b = 4; c = -103;
Δ = b2-4ac
Δ = 42-4·16·(-103)
Δ = 6608
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:

$\sqrt{\Delta}=\sqrt{6608}=\sqrt{16*413}=\sqrt{16}*\sqrt{413}=4\sqrt{413}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{413}}{2*16}=\frac{-4-4\sqrt{413}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{413}}{2*16}=\frac{-4+4\sqrt{413}}{32}
$