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6x^2+4x-5=4x^2-9x
We move all terms to the left:
6x^2+4x-5-(4x^2-9x)=0
We get rid of parentheses
6x^2-4x^2+4x+9x-5=0
We add all the numbers together, and all the variables
2x^2+13x-5=0
a = 2; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·2·(-5)
Δ = 209
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{-(13)-\sqrt{209}}{2*2}=\frac{-13-\sqrt{209}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{209}}{2*2}=\frac{-13+\sqrt{209}}{4} $
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