(4x+7)(7x-38)=180

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Solution for (4x+7)(7x-38)=180 equation:



(4x+7)(7x-38)=180
We move all terms to the left:
(4x+7)(7x-38)-(180)=0
We multiply parentheses ..
(+28x^2-152x+49x-266)-180=0
We get rid of parentheses
28x^2-152x+49x-266-180=0
We add all the numbers together, and all the variables
28x^2-103x-446=0
a = 28; b = -103; c = -446;
Δ = b2-4ac
Δ = -1032-4·28·(-446)
Δ = 60561
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:
$\sqrt{\Delta}=\sqrt{60561}=\sqrt{9*6729}=\sqrt{9}*\sqrt{6729}=3\sqrt{6729}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-103)-3\sqrt{6729}}{2*28}=\frac{103-3\sqrt{6729}}{56} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-103)+3\sqrt{6729}}{2*28}=\frac{103+3\sqrt{6729}}{56} $

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