(5x+9)(2x+10)=78

Solution for (5x+9)(2x+10)=78 equation:

(5x+9)(2x+10)=78

We move all terms to the left:

(5x+9)(2x+10)-(78)=0

We multiply parentheses ..

(+10x^2+50x+18x+90)-78=0

We get rid of parentheses

10x^2+50x+18x+90-78=0

We add all the numbers together, and all the variables

10x^2+68x+12=0

a = 10; b = 68; c = +12;
Δ = b2-4ac
Δ = 682-4·10·12
Δ = 4144
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:

$\sqrt{\Delta}=\sqrt{4144}=\sqrt{16*259}=\sqrt{16}*\sqrt{259}=4\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{259}}{2*10}=\frac{-68-4\sqrt{259}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{259}}{2*10}=\frac{-68+4\sqrt{259}}{20}
$