Question

Use the quadratic formula to solve -5x^2-12x+8=0

Answer 1

`\text{The quadratic formula:}\\\\ax^2+bx+c=0\\\\x_1=(-b-√(b^2-4ac))/(2a);\ x_2=(-b+√(b^2-4ac))/(2a)\\--------------------------------\\\text{We have}\ -5x^2-12x+8=0\\\\a=-5,\ b=-12,\ c=8\\\\\text{Substitute:}\\\\b^2-4ac=(-12)^2-4(-5)(8)=144+160=304\\\\√(b^2-4ac)=√(304)=√(16\cdot9)=√(16)\cdot√(19)=4√(19)\\\\x_1=(-(-12)-4√(19))/(2(-5))=(12-4√(19))/(-10)=\boxed{-(6-2√(19))/(5)}\\\\x_2=(-(-12)+4√(19))/(2(-5))=(12+4√(19))/(-10)=\boxed{-(6+2√(19))/(5)}`