Решение систем уравнений второй степени

$\left \{ {{x+y=-7} \atop {-2 x^{2} +9 y^{2}=-119 }} \right. \\ \\ \left \{ {{y=-7-x} \atop {-2 x^{2}+9 (-7-y)^{2}=-119 }} \right. \\ \\ \left \{ {{y=-7-x} \atop {-2x^{2}+9 (49+14x+ x^{2} )=-119 }} \right. \\ \\ \left \{ {{y=-7-x} \atop {7 x^{2} +126x+441=-119}} \right. \\ \\ \left \{ {{y=-7-x} \atop {7 x^{2}+126x+322=0 }} \right. \\ \\ \left \{ {{y=-7-x} \atop {x^{2}+18x+46=0}} \right$

Решаем квадратное уравнение

$x^{2} +18x+46=0 \\ \\ D= b^{2} -4ac= 18^{2} -4*1*46=324-184=140 \\ \\ x_{1} = \frac{-18- \sqrt{140} }{2*1} =-9- \sqrt{35} \\ \\ x_{2} = \frac{-18+ \sqrt{140} }{2*1} =-9+ \sqrt{35} \\ \\ \left \{ {{ y_{1} =-16- \sqrt{35} } \atop { x_{1}=-9- \sqrt{35} }} \right \\ \\ \left \{ {{y_{2} =2+ \sqrt{35} } \atop { x_{2} =2-\sqrt{35}}} \right.$

Вроде так.

$\sqrt{35} =5.916079783099616$