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5x+69=2x^2-14x+9
We move all terms to the left:
5x+69-(2x^2-14x+9)=0
We get rid of parentheses
-2x^2+5x+14x-9+69=0
We add all the numbers together, and all the variables
-2x^2+19x+60=0
a = -2; b = 19; c = +60;
Δ = b2-4ac
Δ = 192-4·(-2)·60
Δ = 841
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-29}{2*-2}=\frac{-48}{-4} =+12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+29}{2*-2}=\frac{10}{-4} =-2+1/2 $
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