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5x^2-7x=6x+4
We move all terms to the left:
5x^2-7x-(6x+4)=0
We get rid of parentheses
5x^2-7x-6x-4=0
We add all the numbers together, and all the variables
5x^2-13x-4=0
a = 5; b = -13; c = -4;
Δ = b2-4ac
Δ = -132-4·5·(-4)
Δ = 249
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{249}}{2*5}=\frac{13-\sqrt{249}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{249}}{2*5}=\frac{13+\sqrt{249}}{10} $
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