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4x^2+54x+110=14x+614x+6
We move all terms to the left:
4x^2+54x+110-(14x+614x+6)=0
We add all the numbers together, and all the variables
4x^2+54x-(628x+6)+110=0
We get rid of parentheses
4x^2+54x-628x-6+110=0
We add all the numbers together, and all the variables
4x^2-574x+104=0
a = 4; b = -574; c = +104;
Δ = b2-4ac
Δ = -5742-4·4·104
Δ = 327812
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{327812}=\sqrt{4*81953}=\sqrt{4}*\sqrt{81953}=2\sqrt{81953}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-574)-2\sqrt{81953}}{2*4}=\frac{574-2\sqrt{81953}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-574)+2\sqrt{81953}}{2*4}=\frac{574+2\sqrt{81953}}{8} $
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