4a^2+42a-270=0

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Solution for 4a^2+42a-270=0 equation:



4a^2+42a-270=0
a = 4; b = 42; c = -270;
Δ = b2-4ac
Δ = 422-4·4·(-270)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-78}{2*4}=\frac{-120}{8} =-15 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+78}{2*4}=\frac{36}{8} =4+1/2 $

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