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9x(x+3)=7x+9-4
We move all terms to the left:
9x(x+3)-(7x+9-4)=0
We add all the numbers together, and all the variables
9x(x+3)-(7x+5)=0
We multiply parentheses
9x^2+27x-(7x+5)=0
We get rid of parentheses
9x^2+27x-7x-5=0
We add all the numbers together, and all the variables
9x^2+20x-5=0
a = 9; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·9·(-5)
Δ = 580
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{145}}{2*9}=\frac{-20-2\sqrt{145}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{145}}{2*9}=\frac{-20+2\sqrt{145}}{18} $
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