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3=x2+5x-4
We move all terms to the left:
3-(x2+5x-4)=0
We add all the numbers together, and all the variables
-(+x^2+5x-4)+3=0
We get rid of parentheses
-x^2-5x+4+3=0
We add all the numbers together, and all the variables
-1x^2-5x+7=0
a = -1; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-1)·7
Δ = 53
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{53}}{2*-1}=\frac{5-\sqrt{53}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*-1}=\frac{5+\sqrt{53}}{-2} $
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