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(2x^2)-9x-6=4x-3
We move all terms to the left:
(2x^2)-9x-6-(4x-3)=0
We get rid of parentheses
2x^2-9x-4x+3-6=0
We add all the numbers together, and all the variables
2x^2-13x-3=0
a = 2; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·2·(-3)
Δ = 193
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{193}}{2*2}=\frac{13-\sqrt{193}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{193}}{2*2}=\frac{13+\sqrt{193}}{4} $
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