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(6x-1)(4x+1)=90
We move all terms to the left:
(6x-1)(4x+1)-(90)=0
We multiply parentheses ..
(+24x^2+6x-4x-1)-90=0
We get rid of parentheses
24x^2+6x-4x-1-90=0
We add all the numbers together, and all the variables
24x^2+2x-91=0
a = 24; b = 2; c = -91;
Δ = b2-4ac
Δ = 22-4·24·(-91)
Δ = 8740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8740}=\sqrt{4*2185}=\sqrt{4}*\sqrt{2185}=2\sqrt{2185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2185}}{2*24}=\frac{-2-2\sqrt{2185}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2185}}{2*24}=\frac{-2+2\sqrt{2185}}{48} $
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