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5x^2-2(x-1)=3x+4
We move all terms to the left:
5x^2-2(x-1)-(3x+4)=0
We multiply parentheses
5x^2-2x-(3x+4)+2=0
We get rid of parentheses
5x^2-2x-3x-4+2=0
We add all the numbers together, and all the variables
5x^2-5x-2=0
a = 5; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·5·(-2)
Δ = 65
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{-(-5)-\sqrt{65}}{2*5}=\frac{5-\sqrt{65}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*5}=\frac{5+\sqrt{65}}{10} $
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