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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^2-12x+6=0
a = -9; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·(-9)·6
Δ = 360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{10}}{2*-9}=\frac{12-6\sqrt{10}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{10}}{2*-9}=\frac{12+6\sqrt{10}}{-18} $
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