(9x+4)(16x-4)=90

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Solution for (9x+4)(16x-4)=90 equation:



(9x+4)(16x-4)=90
We move all terms to the left:
(9x+4)(16x-4)-(90)=0
We multiply parentheses ..
(+144x^2-36x+64x-16)-90=0
We get rid of parentheses
144x^2-36x+64x-16-90=0
We add all the numbers together, and all the variables
144x^2+28x-106=0
a = 144; b = 28; c = -106;
Δ = b2-4ac
Δ = 282-4·144·(-106)
Δ = 61840
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:
$\sqrt{\Delta}=\sqrt{61840}=\sqrt{16*3865}=\sqrt{16}*\sqrt{3865}=4\sqrt{3865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{3865}}{2*144}=\frac{-28-4\sqrt{3865}}{288} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{3865}}{2*144}=\frac{-28+4\sqrt{3865}}{288} $

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