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8x^2-4x-525=0
a = 8; b = -4; c = -525;
Δ = b2-4ac
Δ = -42-4·8·(-525)
Δ = 16816
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16816}=\sqrt{16*1051}=\sqrt{16}*\sqrt{1051}=4\sqrt{1051}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{1051}}{2*8}=\frac{4-4\sqrt{1051}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{1051}}{2*8}=\frac{4+4\sqrt{1051}}{16} $
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