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3x(x+9)=8x+7
We move all terms to the left:
3x(x+9)-(8x+7)=0
We multiply parentheses
3x^2+27x-(8x+7)=0
We get rid of parentheses
3x^2+27x-8x-7=0
We add all the numbers together, and all the variables
3x^2+19x-7=0
a = 3; b = 19; c = -7;
Δ = b2-4ac
Δ = 192-4·3·(-7)
Δ = 445
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{-(19)-\sqrt{445}}{2*3}=\frac{-19-\sqrt{445}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{445}}{2*3}=\frac{-19+\sqrt{445}}{6} $
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