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X^2=11-4X
We move all terms to the left:
X^2-(11-4X)=0
We add all the numbers together, and all the variables
X^2-(-4X+11)=0
We get rid of parentheses
X^2+4X-11=0
a = 1; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·1·(-11)
Δ = 60
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{15}}{2*1}=\frac{-4-2\sqrt{15}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{15}}{2*1}=\frac{-4+2\sqrt{15}}{2} $
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