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1.5x^2+x^2-100=0
We add all the numbers together, and all the variables
2.5x^2-100=0
a = 2.5; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·2.5·(-100)
Δ = 1000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{10}}{2*2.5}=\frac{0-10\sqrt{10}}{5} =-\frac{10\sqrt{10}}{5} =-2\sqrt{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{10}}{2*2.5}=\frac{0+10\sqrt{10}}{5} =\frac{10\sqrt{10}}{5} =2\sqrt{10} $
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