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x2-76x+13=0
We add all the numbers together, and all the variables
x^2-76x+13=0
a = 1; b = -76; c = +13;
Δ = b2-4ac
Δ = -762-4·1·13
Δ = 5724
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5724}=\sqrt{36*159}=\sqrt{36}*\sqrt{159}=6\sqrt{159}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-6\sqrt{159}}{2*1}=\frac{76-6\sqrt{159}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+6\sqrt{159}}{2*1}=\frac{76+6\sqrt{159}}{2} $
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