(x-4)(2x+10)=153

Solution for (x-4)(2x+10)=153 equation:

(x-4)(2x+10)=153

We move all terms to the left:

(x-4)(2x+10)-(153)=0

We multiply parentheses ..

(+2x^2+10x-8x-40)-153=0

We get rid of parentheses

2x^2+10x-8x-40-153=0

We add all the numbers together, and all the variables

2x^2+2x-193=0

a = 2; b = 2; c = -193;
Δ = b2-4ac
Δ = 22-4·2·(-193)
Δ = 1548
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:

$\sqrt{\Delta}=\sqrt{1548}=\sqrt{36*43}=\sqrt{36}*\sqrt{43}=6\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{43}}{2*2}=\frac{-2-6\sqrt{43}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{43}}{2*2}=\frac{-2+6\sqrt{43}}{4}
$