giopizza02
14

# What two numbers that if multiplied equal -90 and if added equal 8?

$x-first\ number\\y-second\ number\\\\ \left \{ {{x\cdot\ y=-90} \atop {x+y=8}} \right.\\\\From\ second\ equayion:\\x=8-y\\\\Substracted\ to\ first\ equation:\\(8-y)y=-90\\-y^2+8y+90=0\\\\\Delta=b^2-4ac\\\Delta=8^2-4\cdot(-1)\cdot90=64+360=424\\\sqrt{\Delta}=\sqrt{424}2\sqrt{106}\\\\y_1=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-8+2\sqrt{106}}{2\cdot(-1)}=4-\sqrt{106}\\y_2=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-8-2\sqrt{106}}{2\cdot(-1)}=4+\sqrt{106}\\\\x_1=8-(4-\sqrt{106})=8-4+\sqrt{106}=4+\sqrt{106}$ $x_2=8-(4-+\sqrt{106})=8-4-\sqrt{106}=4-\sqrt{106}\\\\ \left \{ {{y=4-\sqrt{106}} \atop {x=4+\sqrt{106}}} \right.\\$