0=4x^2+51x-135

Solution for 0=4x^2+51x-135 equation:

0=4x^2+51x-135

We move all terms to the left:

0-(4x^2+51x-135)=0

We add all the numbers together, and all the variables

-(4x^2+51x-135)=0

We get rid of parentheses

-4x^2-51x+135=0

a = -4; b = -51; c = +135;
Δ = b2-4ac
Δ = -512-4·(-4)·135
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-69}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+69}{2*-4}=\frac{120}{-8}
=-15
$