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4x^2+21x=-3x+11
We move all terms to the left:
4x^2+21x-(-3x+11)=0
We get rid of parentheses
4x^2+21x+3x-11=0
We add all the numbers together, and all the variables
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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