Enter the coefficients a, b, c of quadratic equation in its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.
Calculation:
140=3∗sqrt(3)∗a2+30a−5.19615242271a2−30a+140=05.19615242271a2+30a−140=0p=5.19615242271;q=30;r=−140D=q2−4pr=302−4⋅5.19615242271⋅(−140)=3809.84535672D>0a1,2=2p−q±D=10.3923048454−30±3809.85a1,2=−2.88675135±5.93938935376a1=3.05263800781a2=−8.8261406997 Factored form of the equation: 5.19615242271(a−3.05263800781)(a+8.8261406997)=0
Solution in text:
-5.19615242271a2-30a+140=0 ... quadratic equation
Discriminant: D = b2 - 4ac = 3809.84535672 D>0 ... The equation has two distinct real roots