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4x^2+32x+7=0
a = 4; b = 32; c = +7;
Δ = b2-4ac
Δ = 322-4·4·7
Δ = 912
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{57}}{2*4}=\frac{-32-4\sqrt{57}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{57}}{2*4}=\frac{-32+4\sqrt{57}}{8} $
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