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4x^2=41-8x
We move all terms to the left:
4x^2-(41-8x)=0
We add all the numbers together, and all the variables
4x^2-(-8x+41)=0
We get rid of parentheses
4x^2+8x-41=0
a = 4; b = 8; c = -41;
Δ = b2-4ac
Δ = 82-4·4·(-41)
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{5}}{2*4}=\frac{-8-12\sqrt{5}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{5}}{2*4}=\frac{-8+12\sqrt{5}}{8} $
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