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4x(5+6x)=212
We move all terms to the left:
4x(5+6x)-(212)=0
We add all the numbers together, and all the variables
4x(6x+5)-212=0
We multiply parentheses
24x^2+20x-212=0
a = 24; b = 20; c = -212;
Δ = b2-4ac
Δ = 202-4·24·(-212)
Δ = 20752
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20752}=\sqrt{16*1297}=\sqrt{16}*\sqrt{1297}=4\sqrt{1297}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{1297}}{2*24}=\frac{-20-4\sqrt{1297}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{1297}}{2*24}=\frac{-20+4\sqrt{1297}}{48} $
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