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8x^2+5x-9=6x-4
We move all terms to the left:
8x^2+5x-9-(6x-4)=0
We get rid of parentheses
8x^2+5x-6x+4-9=0
We add all the numbers together, and all the variables
8x^2-1x-5=0
a = 8; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·8·(-5)
Δ = 161
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{-(-1)-\sqrt{161}}{2*8}=\frac{1-\sqrt{161}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161}}{2*8}=\frac{1+\sqrt{161}}{16} $
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