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7-9x^2=5x-6
We move all terms to the left:
7-9x^2-(5x-6)=0
We get rid of parentheses
-9x^2-5x+6+7=0
We add all the numbers together, and all the variables
-9x^2-5x+13=0
a = -9; b = -5; c = +13;
Δ = b2-4ac
Δ = -52-4·(-9)·13
Δ = 493
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{-(-5)-\sqrt{493}}{2*-9}=\frac{5-\sqrt{493}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{493}}{2*-9}=\frac{5+\sqrt{493}}{-18} $
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