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70x-9x^2=5x-6
We move all terms to the left:
70x-9x^2-(5x-6)=0
We get rid of parentheses
-9x^2+70x-5x+6=0
We add all the numbers together, and all the variables
-9x^2+65x+6=0
a = -9; b = 65; c = +6;
Δ = b2-4ac
Δ = 652-4·(-9)·6
Δ = 4441
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{-(65)-\sqrt{4441}}{2*-9}=\frac{-65-\sqrt{4441}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4441}}{2*-9}=\frac{-65+\sqrt{4441}}{-18} $
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