(6+2x)(2x+25)=102

Solution for (6+2x)(2x+25)=102 equation:

(6+2x)(2x+25)=102

We move all terms to the left:

(6+2x)(2x+25)-(102)=0

We add all the numbers together, and all the variables

(2x+6)(2x+25)-102=0

We multiply parentheses ..

(+4x^2+50x+12x+150)-102=0

We get rid of parentheses

4x^2+50x+12x+150-102=0

We add all the numbers together, and all the variables

4x^2+62x+48=0

a = 4; b = 62; c = +48;
Δ = b2-4ac
Δ = 622-4·4·48
Δ = 3076
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:

$\sqrt{\Delta}=\sqrt{3076}=\sqrt{4*769}=\sqrt{4}*\sqrt{769}=2\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{769}}{2*4}=\frac{-62-2\sqrt{769}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{769}}{2*4}=\frac{-62+2\sqrt{769}}{8}
$