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7x+9x^2=5x+6
We move all terms to the left:
7x+9x^2-(5x+6)=0
We get rid of parentheses
9x^2+7x-5x-6=0
We add all the numbers together, and all the variables
9x^2+2x-6=0
a = 9; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·9·(-6)
Δ = 220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*9}=\frac{-2-2\sqrt{55}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*9}=\frac{-2+2\sqrt{55}}{18} $
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