(4x+17)(2x+7)=180

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Solution for (4x+17)(2x+7)=180 equation:



(4x+17)(2x+7)=180
We move all terms to the left:
(4x+17)(2x+7)-(180)=0
We multiply parentheses ..
(+8x^2+28x+34x+119)-180=0
We get rid of parentheses
8x^2+28x+34x+119-180=0
We add all the numbers together, and all the variables
8x^2+62x-61=0
a = 8; b = 62; c = -61;
Δ = b2-4ac
Δ = 622-4·8·(-61)
Δ = 5796
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:
$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-6\sqrt{161}}{2*8}=\frac{-62-6\sqrt{161}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+6\sqrt{161}}{2*8}=\frac{-62+6\sqrt{161}}{16} $

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