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4x^2=6x+1/4
We move all terms to the left:
4x^2-(6x+1/4)=0
We add all the numbers together, and all the variables
4x^2-(+6x+1/4)=0
We get rid of parentheses
4x^2-6x-1/4=0
We multiply all the terms by the denominator
4x^2*4-6x*4-1=0
Wy multiply elements
16x^2-24x-1=0
a = 16; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·16·(-1)
Δ = 640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{10}}{2*16}=\frac{24-8\sqrt{10}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{10}}{2*16}=\frac{24+8\sqrt{10}}{32} $
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