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8x^2+46x-63=0
a = 8; b = 46; c = -63;
Δ = b2-4ac
Δ = 462-4·8·(-63)
Δ = 4132
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4132}=\sqrt{4*1033}=\sqrt{4}*\sqrt{1033}=2\sqrt{1033}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{1033}}{2*8}=\frac{-46-2\sqrt{1033}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{1033}}{2*8}=\frac{-46+2\sqrt{1033}}{16} $
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