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2a^2+10a+13=25
We move all terms to the left:
2a^2+10a+13-(25)=0
We add all the numbers together, and all the variables
2a^2+10a-12=0
a = 2; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·2·(-12)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{196}=14$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*2}=\frac{-24}{4} =-6 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*2}=\frac{4}{4} =1 $
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