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4x^2+22x-23=0
a = 4; b = 22; c = -23;
Δ = b2-4ac
Δ = 222-4·4·(-23)
Δ = 852
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{213}}{2*4}=\frac{-22-2\sqrt{213}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{213}}{2*4}=\frac{-22+2\sqrt{213}}{8} $
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