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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x-(5x(x+10))+30=0


We calculate terms in parentheses: -(5x(x+10)), so:

5x(x+10)

We multiply parentheses

5x^2+50x

Back to the equation:

-(5x^2+50x)


We get rid of parentheses

-5x^2+7x-50x+30=0

We add all the numbers together, and all the variables

-5x^2-43x+30=0

a = -5; b = -43; c = +30;
Δ = b2-4ac
Δ = -432-4·(-5)·30
Δ = 2449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{2449}}{2*-5}=\frac{43-\sqrt{2449}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{2449}}{2*-5}=\frac{43+\sqrt{2449}}{-10}
$