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10x^2-76x+84=0
a = 10; b = -76; c = +84;
Δ = b2-4ac
Δ = -762-4·10·84
Δ = 2416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{151}}{2*10}=\frac{76-4\sqrt{151}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{151}}{2*10}=\frac{76+4\sqrt{151}}{20} $
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