15a2-3a=3-7a

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Solution for 15a2-3a=3-7a equation:



15a^2-3a=3-7a
We move all terms to the left:
15a^2-3a-(3-7a)=0
We add all the numbers together, and all the variables
15a^2-3a-(-7a+3)=0
We get rid of parentheses
15a^2-3a+7a-3=0
We add all the numbers together, and all the variables
15a^2+4a-3=0
a = 15; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·15·(-3)
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{-(4)-14}{2*15}=\frac{-18}{30} =-3/5 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*15}=\frac{10}{30} =1/3 $

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