4x^2+3x=45

Solution for 4x^2+3x=45 equation:

4x^2+3x=45

We move all terms to the left:

4x^2+3x-(45)=0

a = 4; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·4·(-45)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*4}=\frac{-30}{8}
=-3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*4}=\frac{24}{8}
=3
$