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(2x^2-3x+7)-(5x^2-8x-9)=0
We get rid of parentheses
2x^2-5x^2-3x+8x+7+9=0
We add all the numbers together, and all the variables
-3x^2+5x+16=0
a = -3; b = 5; c = +16;
Δ = b2-4ac
Δ = 52-4·(-3)·16
Δ = 217
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{217}}{2*-3}=\frac{-5-\sqrt{217}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{217}}{2*-3}=\frac{-5+\sqrt{217}}{-6} $
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