(9x+4)(7x+32)=180

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Solution for (9x+4)(7x+32)=180 equation:



(9x+4)(7x+32)=180
We move all terms to the left:
(9x+4)(7x+32)-(180)=0
We multiply parentheses ..
(+63x^2+288x+28x+128)-180=0
We get rid of parentheses
63x^2+288x+28x+128-180=0
We add all the numbers together, and all the variables
63x^2+316x-52=0
a = 63; b = 316; c = -52;
Δ = b2-4ac
Δ = 3162-4·63·(-52)
Δ = 112960
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:
$\sqrt{\Delta}=\sqrt{112960}=\sqrt{64*1765}=\sqrt{64}*\sqrt{1765}=8\sqrt{1765}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(316)-8\sqrt{1765}}{2*63}=\frac{-316-8\sqrt{1765}}{126} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(316)+8\sqrt{1765}}{2*63}=\frac{-316+8\sqrt{1765}}{126} $

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