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4x^2-8x-10=12
We move all terms to the left:
4x^2-8x-10-(12)=0
We add all the numbers together, and all the variables
4x^2-8x-22=0
a = 4; b = -8; c = -22;
Δ = b2-4ac
Δ = -82-4·4·(-22)
Δ = 416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{26}}{2*4}=\frac{8-4\sqrt{26}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{26}}{2*4}=\frac{8+4\sqrt{26}}{8} $
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