(6x+5)(8x-37)=180

Solution for (6x+5)(8x-37)=180 equation:

(6x+5)(8x-37)=180

We move all terms to the left:

(6x+5)(8x-37)-(180)=0

We multiply parentheses ..

(+48x^2-222x+40x-185)-180=0

We get rid of parentheses

48x^2-222x+40x-185-180=0

We add all the numbers together, and all the variables

48x^2-182x-365=0

a = 48; b = -182; c = -365;
Δ = b2-4ac
Δ = -1822-4·48·(-365)
Δ = 103204
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:

$\sqrt{\Delta}=\sqrt{103204}=\sqrt{4*25801}=\sqrt{4}*\sqrt{25801}=2\sqrt{25801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-2\sqrt{25801}}{2*48}=\frac{182-2\sqrt{25801}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+2\sqrt{25801}}{2*48}=\frac{182+2\sqrt{25801}}{96}
$