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5x^2+6x^2=143
We move all terms to the left:
5x^2+6x^2-(143)=0
We add all the numbers together, and all the variables
11x^2-143=0
a = 11; b = 0; c = -143;
Δ = b2-4ac
Δ = 02-4·11·(-143)
Δ = 6292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6292}=\sqrt{484*13}=\sqrt{484}*\sqrt{13}=22\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{13}}{2*11}=\frac{0-22\sqrt{13}}{22} =-\frac{22\sqrt{13}}{22} =-\sqrt{13} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{13}}{2*11}=\frac{0+22\sqrt{13}}{22} =\frac{22\sqrt{13}}{22} =\sqrt{13} $
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