R(x)=4x^2+5x-6

Solution for R(x)=4x^2+5x-6 equation:

(R)=4R^2+5R-6

We move all terms to the left:

(R)-(4R^2+5R-6)=0

We get rid of parentheses

-4R^2+R-5R+6=0

We add all the numbers together, and all the variables

-4R^2-4R+6=0

a = -4; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-4)·6
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-4}=\frac{4-4\sqrt{7}}{-8}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-4}=\frac{4+4\sqrt{7}}{-8}
$