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2x^2-5x-3=6/7
We move all terms to the left:
2x^2-5x-3-(6/7)=0
We add all the numbers together, and all the variables
2x^2-5x-3-(+6/7)=0
We get rid of parentheses
2x^2-5x-3-6/7=0
We multiply all the terms by the denominator
2x^2*7-5x*7-6-3*7=0
We add all the numbers together, and all the variables
2x^2*7-5x*7-27=0
Wy multiply elements
14x^2-35x-27=0
a = 14; b = -35; c = -27;
Δ = b2-4ac
Δ = -352-4·14·(-27)
Δ = 2737
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{-(-35)-\sqrt{2737}}{2*14}=\frac{35-\sqrt{2737}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2737}}{2*14}=\frac{35+\sqrt{2737}}{28} $
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