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X2+6X=11/4
We move all terms to the left:
X2+6X-(11/4)=0
We add all the numbers together, and all the variables
X2+6X-(+11/4)=0
We add all the numbers together, and all the variables
X^2+6X-(+11/4)=0
We get rid of parentheses
X^2+6X-11/4=0
We multiply all the terms by the denominator
X^2*4+6X*4-11=0
Wy multiply elements
4X^2+24X-11=0
a = 4; b = 24; c = -11;
Δ = b2-4ac
Δ = 242-4·4·(-11)
Δ = 752
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{47}}{2*4}=\frac{-24-4\sqrt{47}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{47}}{2*4}=\frac{-24+4\sqrt{47}}{8} $
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