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19x-13=7+2x^2
We move all terms to the left:
19x-13-(7+2x^2)=0
We get rid of parentheses
-2x^2+19x-7-13=0
We add all the numbers together, and all the variables
-2x^2+19x-20=0
a = -2; b = 19; c = -20;
Δ = b2-4ac
Δ = 192-4·(-2)·(-20)
Δ = 201
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{-(19)-\sqrt{201}}{2*-2}=\frac{-19-\sqrt{201}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{201}}{2*-2}=\frac{-19+\sqrt{201}}{-4} $
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