10(x+7)(x-5)=3x(x+7)

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

10(x+7)(x-5)=3x(x+7)

We move all terms to the left:

10(x+7)(x-5)-(3x(x+7))=0

We multiply parentheses ..

10(+x^2-5x+7x-35)-(3x(x+7))=0


We calculate terms in parentheses: -(3x(x+7)), so:

3x(x+7)

We multiply parentheses

3x^2+21x

Back to the equation:

-(3x^2+21x)


We multiply parentheses

10x^2-50x+70x-(3x^2+21x)-350=0

We get rid of parentheses

10x^2-3x^2-50x+70x-21x-350=0

We add all the numbers together, and all the variables

7x^2-1x-350=0

a = 7; b = -1; c = -350;
Δ = b2-4ac
Δ = -12-4·7·(-350)
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-99}{2*7}=\frac{-98}{14}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+99}{2*7}=\frac{100}{14}
=7+1/7
$