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5x^2-55=90
We move all terms to the left:
5x^2-55-(90)=0
We add all the numbers together, and all the variables
5x^2-145=0
a = 5; b = 0; c = -145;
Δ = b2-4ac
Δ = 02-4·5·(-145)
Δ = 2900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{29}}{2*5}=\frac{0-10\sqrt{29}}{10} =-\frac{10\sqrt{29}}{10} =-\sqrt{29} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{29}}{2*5}=\frac{0+10\sqrt{29}}{10} =\frac{10\sqrt{29}}{10} =\sqrt{29} $
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