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5x*5x+7=22
We move all terms to the left:
5x*5x+7-(22)=0
We add all the numbers together, and all the variables
5x*5x-15=0
Wy multiply elements
25x^2-15=0
a = 25; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·25·(-15)
Δ = 1500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{15}}{2*25}=\frac{0-10\sqrt{15}}{50} =-\frac{10\sqrt{15}}{50} =-\frac{\sqrt{15}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{15}}{2*25}=\frac{0+10\sqrt{15}}{50} =\frac{10\sqrt{15}}{50} =\frac{\sqrt{15}}{5} $
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