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4x^2+2=8+3x
We move all terms to the left:
4x^2+2-(8+3x)=0
We add all the numbers together, and all the variables
4x^2-(3x+8)+2=0
We get rid of parentheses
4x^2-3x-8+2=0
We add all the numbers together, and all the variables
4x^2-3x-6=0
a = 4; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·4·(-6)
Δ = 105
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{105}}{2*4}=\frac{3-\sqrt{105}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*4}=\frac{3+\sqrt{105}}{8} $
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