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3x(x+16/4)=6x+22
We move all terms to the left:
3x(x+16/4)-(6x+22)=0
We add all the numbers together, and all the variables
3x(x+4)-(6x+22)=0
We multiply parentheses
3x^2+12x-(6x+22)=0
We get rid of parentheses
3x^2+12x-6x-22=0
We add all the numbers together, and all the variables
3x^2+6x-22=0
a = 3; b = 6; c = -22;
Δ = b2-4ac
Δ = 62-4·3·(-22)
Δ = 300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10\sqrt{3}}{2*3}=\frac{-6-10\sqrt{3}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10\sqrt{3}}{2*3}=\frac{-6+10\sqrt{3}}{6} $
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