Question

Решите уравнение через дискриминант:
3a^2+a=7
2a^2-a=3​

Answer 1

$1)3a^{2}+a=7\\\\3a^{2}+a-7=0\\\\D=1^{2}-4*3*(-7)=1+84=85\\\\\boxed{a_{1}=\frac{-1-\sqrt{85}}{6}}\\\\\boxed{a_{2}=\frac{-1+\sqrt{85}}{6}} \\\\\\2)2a^{2}-a=3\\\\2a^{2}-a-3=0\\\\D=(-1)^{2}-4*2*(-3)=1+24=25=5^{2}\\\\a_{1}=\frac{1-5}{4} =\boxed{-1}\\\\a_{2}=\frac{1+5}{4}=\boxed{1,5}$

$3)\frac{1}{4}x^{2}-x+1=0|*4\\\\x^{2}-4x+4=0\\\\(x-2)^{2}=0\\\\x-2=0\\\\\boxed{x=2}\\\\\\4)4a^{2}-5=a\\\\4a^{2}-a-5=0\\\\D=(-1)^{2}-4*4*(-5)=1+80=81=9^{2}\\\\a_{1}=\frac{1-9}{8} =\boxed{-1}\\\\a_{2}=\frac{1+9}{8}=\boxed{1,25}$