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(X+5)2=10X^2-6X-1
We move all terms to the left:
(X+5)2-(10X^2-6X-1)=0
We multiply parentheses
2X-(10X^2-6X-1)+10=0
We get rid of parentheses
-10X^2+2X+6X+1+10=0
We add all the numbers together, and all the variables
-10X^2+8X+11=0
a = -10; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-10)·11
Δ = 504
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{14}}{2*-10}=\frac{-8-6\sqrt{14}}{-20} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{14}}{2*-10}=\frac{-8+6\sqrt{14}}{-20} $
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