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3x(7x+9)=3-x
We move all terms to the left:
3x(7x+9)-(3-x)=0
We add all the numbers together, and all the variables
3x(7x+9)-(-1x+3)=0
We multiply parentheses
21x^2+27x-(-1x+3)=0
We get rid of parentheses
21x^2+27x+1x-3=0
We add all the numbers together, and all the variables
21x^2+28x-3=0
a = 21; b = 28; c = -3;
Δ = b2-4ac
Δ = 282-4·21·(-3)
Δ = 1036
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{259}}{2*21}=\frac{-28-2\sqrt{259}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{259}}{2*21}=\frac{-28+2\sqrt{259}}{42} $
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