Решите уравнение [latex] \int\limits^x_1 {(1-4t)} \, dt =12-9x[/latex]

[latex]\displaystyle \int\limits^x_1 {(1-4t)} \, dt =12-9x\\ \left[t-2t^2\right]_1^x=12-9x\\ x-2x^2-(1-2\cdot1^2)=12-9x\\ x-2x^2+1=12-9x\\ 2x^2-10x+11=0\\ \Delta=(-10)^2-4\cdot2\cdot11=100-88=12\\ \sqrt{\Delta}=\sqrt{12}=2\sqrt3\\ x_1=\dfrac{-(-10)-2\sqrt3}{2\cdot2}=\dfrac{5-\sqrt3}{2}\\ x_2=\dfrac{-(-10)+2\sqrt3}{2\cdot2}=\dfrac{5+\sqrt3}{2}\\\\ \boxed{x=\left\{\dfrac{5-\sqrt3}{2},\dfrac{5+\sqrt3}{2}\right\}}[/latex]