The quadratic equation can be used to find the solution to any polynomial equation of the form a*(x^2) + b*x+c = 0. The roots are (-b (+/-) sqrt(b^2 - (4*a*c)))/2a. In this case, assuming the equation was supposed to read (x^2) + 5x - 6, the solutions are
(-5 (+/-) sqrt (5^2 - (4*1*-6))/2
(-5 (+/-) sqrt (25 - (-24))/2
(-5 (+/-) sqrt (25 + 24))/2
(-5 (+/-) sqrt (49))/2
(-5 (+/-) 7)/2
(-5 + 7)/2 and (-5-7)/2
1 and -6.
Or, one can factor the original formula into (x-1)(x+6) = 0, which makes it clear that 1 and -6 are the answers to this problem. More complex quadratics are harder to factor, but the quadratic formula always works.
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5x -3y = -6 -3y = -5x -6 y = 5/3x+2 in slope intercept form
4x - 3 - 5x + 7 = 6 4x - 5x = 3 - 7 + 6 -1x = 2 x = -2
5x - 4 = 3x + 6 5x - 3x = 6 + 4 2x = 10 x = 5
3x + 5x = 2x + 28x = 2x + 26x = 2x = (2/6) = 1/3
4x-7=5x-2 x=-5