(-10+3x)(4-5x)=-30+9x

Solution for (-10+3x)(4-5x)=-30+9x equation:

(-10+3x)(4-5x)=-30+9x

We move all terms to the left:

(-10+3x)(4-5x)-(-30+9x)=0

We add all the numbers together, and all the variables

(3x-10)(-5x+4)-(9x-30)=0

We get rid of parentheses

(3x-10)(-5x+4)-9x+30=0

We multiply parentheses ..

(-15x^2+12x+50x-40)-9x+30=0

We get rid of parentheses

-15x^2+12x+50x-9x-40+30=0

We add all the numbers together, and all the variables

-15x^2+53x-10=0

a = -15; b = 53; c = -10;
Δ = b2-4ac
Δ = 532-4·(-15)·(-10)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-47}{2*-15}=\frac{-100}{-30}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+47}{2*-15}=\frac{-6}{-30}
=1/5
$