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4x^2=14+3x
We move all terms to the left:
4x^2-(14+3x)=0
We add all the numbers together, and all the variables
4x^2-(3x+14)=0
We get rid of parentheses
4x^2-3x-14=0
a = 4; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·4·(-14)
Δ = 233
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{233}}{2*4}=\frac{3-\sqrt{233}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{233}}{2*4}=\frac{3+\sqrt{233}}{8} $
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