(5x+3)(x-6)=5x^=27x-8

Solution for (5x+3)(x-6)=5x^=27x-8 equation:

(5x+3)(x-6)=5x^=27x-8

We move all terms to the left:

(5x+3)(x-6)-(5x^)=0

We add all the numbers together, and all the variables

-5x+(5x+3)(x-6)=0

We multiply parentheses ..

(+5x^2-30x+3x-18)-5x=0

We get rid of parentheses

5x^2-30x+3x-5x-18=0

We add all the numbers together, and all the variables

5x^2-32x-18=0

a = 5; b = -32; c = -18;
Δ = b2-4ac
Δ = -322-4·5·(-18)
Δ = 1384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1384}=\sqrt{4*346}=\sqrt{4}*\sqrt{346}=2\sqrt{346}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{346}}{2*5}=\frac{32-2\sqrt{346}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{346}}{2*5}=\frac{32+2\sqrt{346}}{10}
$