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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+10x^2+50x-18x-90)), so:

(+10x^2+50x-18x-90)

We get rid of parentheses

10x^2+50x-18x-90

We add all the numbers together, and all the variables

10x^2+32x-90

Back to the equation:

-(10x^2+32x-90)


We get rid of parentheses

-10x^2-32x+90+78=0

We add all the numbers together, and all the variables

-10x^2-32x+168=0

a = -10; b = -32; c = +168;
Δ = b2-4ac
Δ = -322-4·(-10)·168
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-88}{2*-10}=\frac{-56}{-20}
=2+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+88}{2*-10}=\frac{120}{-20}
=-6
$