(6x+7)(8x-27)=180

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Solution for (6x+7)(8x-27)=180 equation:



(6x+7)(8x-27)=180
We move all terms to the left:
(6x+7)(8x-27)-(180)=0
We multiply parentheses ..
(+48x^2-162x+56x-189)-180=0
We get rid of parentheses
48x^2-162x+56x-189-180=0
We add all the numbers together, and all the variables
48x^2-106x-369=0
a = 48; b = -106; c = -369;
Δ = b2-4ac
Δ = -1062-4·48·(-369)
Δ = 82084
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:
$\sqrt{\Delta}=\sqrt{82084}=\sqrt{4*20521}=\sqrt{4}*\sqrt{20521}=2\sqrt{20521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{20521}}{2*48}=\frac{106-2\sqrt{20521}}{96} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{20521}}{2*48}=\frac{106+2\sqrt{20521}}{96} $

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