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3x-4=11-4x^2
We move all terms to the left:
3x-4-(11-4x^2)=0
We get rid of parentheses
4x^2+3x-11-4=0
We add all the numbers together, and all the variables
4x^2+3x-15=0
a = 4; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·4·(-15)
Δ = 249
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{249}}{2*4}=\frac{-3-\sqrt{249}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{249}}{2*4}=\frac{-3+\sqrt{249}}{8} $
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