7x*8x=(5x+3)(10x-2)

Solution for 7x*8x=(5x+3)(10x-2) equation:

7x*8x=(5x+3)(10x-2)

We move all terms to the left:

7x*8x-((5x+3)(10x-2))=0

Wy multiply elements

56x^2-((5x+3)(10x-2))=0

We multiply parentheses ..

56x^2-((+50x^2-10x+30x-6))=0


We calculate terms in parentheses: -((+50x^2-10x+30x-6)), so:

(+50x^2-10x+30x-6)

We get rid of parentheses

50x^2-10x+30x-6

We add all the numbers together, and all the variables

50x^2+20x-6

Back to the equation:

-(50x^2+20x-6)


We get rid of parentheses

56x^2-50x^2-20x+6=0

We add all the numbers together, and all the variables

6x^2-20x+6=0

a = 6; b = -20; c = +6;
Δ = b2-4ac
Δ = -202-4·6·6
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*6}=\frac{36}{12}
=3
$