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x2=10x+21=0
We move all terms to the left:
x2-(10x+21)=0
We add all the numbers together, and all the variables
x^2-(10x+21)=0
We get rid of parentheses
x^2-10x-21=0
a = 1; b = -10; c = -21;
Δ = b2-4ac
Δ = -102-4·1·(-21)
Δ = 184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{46}}{2*1}=\frac{10-2\sqrt{46}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{46}}{2*1}=\frac{10+2\sqrt{46}}{2} $
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