Question

Solve the quadratic using the quadratic formula

`5x {}^(2) + 12x - 2 = 0`

Answer 1

The quadratic formula:


`ax^2+bx+c=0\\\\x_1=(-b-√(b^2-4ac))/(2a);\ x_2=(-b+√(b^2-4ac))/(2a)`

We have:


`5x^2+12x-2=0\\\\a=5;\ b=12;\ c=-2\\\\b^2-4ac=12^2-4\cdot5\cdot(-2)=144+40=184\\\\√(b^2-4ac)=√(184)=√(4\cdot46)=2√(46)`

substitute


`x_1=(-12-2√(46))/(2\cdot5)=(-6-√(46))/(5)\\\\x_2=(-12+2√(46))/(2\cdot5)=(-6+√(46))/(5)`