4a^2-29a=-30

Solution for 4a^2-29a=-30 equation:

4a^2-29a=-30

We move all terms to the left:

4a^2-29a-(-30)=0

We add all the numbers together, and all the variables

4a^2-29a+30=0

a = 4; b = -29; c = +30;
Δ = b2-4ac
Δ = -292-4·4·30
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-19}{2*4}=\frac{10}{8}
=1+1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+19}{2*4}=\frac{48}{8}
=6
$