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9x(34x+4)=92+4x
We move all terms to the left:
9x(34x+4)-(92+4x)=0
We add all the numbers together, and all the variables
9x(34x+4)-(4x+92)=0
We multiply parentheses
306x^2+36x-(4x+92)=0
We get rid of parentheses
306x^2+36x-4x-92=0
We add all the numbers together, and all the variables
306x^2+32x-92=0
a = 306; b = 32; c = -92;
Δ = b2-4ac
Δ = 322-4·306·(-92)
Δ = 113632
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{113632}=\sqrt{16*7102}=\sqrt{16}*\sqrt{7102}=4\sqrt{7102}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{7102}}{2*306}=\frac{-32-4\sqrt{7102}}{612} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{7102}}{2*306}=\frac{-32+4\sqrt{7102}}{612} $
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