45x^2-29x=30

Solution for 45x^2-29x=30 equation:

45x^2-29x=30

We move all terms to the left:

45x^2-29x-(30)=0

a = 45; b = -29; c = -30;
Δ = b2-4ac
Δ = -292-4·45·(-30)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-79}{2*45}=\frac{-50}{90}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+79}{2*45}=\frac{108}{90}
=1+1/5
$