(42a^2+55a-25)=0

Solution for (42a^2+55a-25)=0 equation:

(42a^2+55a-25)=0

We get rid of parentheses

42a^2+55a-25=0

a = 42; b = 55; c = -25;
Δ = b2-4ac
Δ = 552-4·42·(-25)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-85}{2*42}=\frac{-140}{84}
=-1+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+85}{2*42}=\frac{30}{84}
=5/14
$