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x2+10x+12=2x+52x+5
We move all terms to the left:
x2+10x+12-(2x+52x+5)=0
We add all the numbers together, and all the variables
x2+10x-(54x+5)+12=0
We add all the numbers together, and all the variables
x^2+10x-(54x+5)+12=0
We get rid of parentheses
x^2+10x-54x-5+12=0
We add all the numbers together, and all the variables
x^2-44x+7=0
a = 1; b = -44; c = +7;
Δ = b2-4ac
Δ = -442-4·1·7
Δ = 1908
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{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-6\sqrt{53}}{2*1}=\frac{44-6\sqrt{53}}{2}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+6\sqrt{53}}{2*1}=\frac{44+6\sqrt{53}}{2}
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