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7x^2+32x+5=0
a = 7; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·7·5
Δ = 884
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{221}}{2*7}=\frac{-32-2\sqrt{221}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{221}}{2*7}=\frac{-32+2\sqrt{221}}{14} $
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