(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+92x-51=0

a = 4; b = 92; c = -51;
Δ = b2-4ac
Δ = 922-4·4·(-51)
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-8\sqrt{145}}{2*4}=\frac{-92-8\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+8\sqrt{145}}{2*4}=\frac{-92+8\sqrt{145}}{8}
$