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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(+50x^2-10x+30x-6)-7x*8x=0

Wy multiply elements

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

We get rid of parentheses

50x^2-56x^2-10x+30x-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{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+16}{2*-6}=\frac{-4}{-12}
=1/3
$