(2x+43)(2x-3)=180

Solution for (2x+43)(2x-3)=180 equation:

(2x+43)(2x-3)=180

We move all terms to the left:

(2x+43)(2x-3)-(180)=0

We multiply parentheses ..

(+4x^2-6x+86x-129)-180=0

We get rid of parentheses

4x^2-6x+86x-129-180=0

We add all the numbers together, and all the variables

4x^2+80x-309=0

a = 4; b = 80; c = -309;
Δ = b2-4ac
Δ = 802-4·4·(-309)
Δ = 11344
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:

$\sqrt{\Delta}=\sqrt{11344}=\sqrt{16*709}=\sqrt{16}*\sqrt{709}=4\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{709}}{2*4}=\frac{-80-4\sqrt{709}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{709}}{2*4}=\frac{-80+4\sqrt{709}}{8}
$