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x^2+5x=21+12x
We move all terms to the left:
x^2+5x-(21+12x)=0
We add all the numbers together, and all the variables
x^2+5x-(12x+21)=0
We get rid of parentheses
x^2+5x-12x-21=0
We add all the numbers together, and all the variables
x^2-7x-21=0
a = 1; b = -7; c = -21;
Δ = b2-4ac
Δ = -72-4·1·(-21)
Δ = 133
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{133}}{2*1}=\frac{7-\sqrt{133}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{133}}{2*1}=\frac{7+\sqrt{133}}{2} $
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