7(x+1)+5x(2-x)=3(x-1)

Solution for 7(x+1)+5x(2-x)=3(x-1) equation:

7(x+1)+5x(2-x)=3(x-1)

We move all terms to the left:

7(x+1)+5x(2-x)-(3(x-1))=0

We add all the numbers together, and all the variables

7(x+1)+5x(-1x+2)-(3(x-1))=0

We multiply parentheses

-5x^2+7x+10x-(3(x-1))+7=0


We calculate terms in parentheses: -(3(x-1)), so:

3(x-1)

We multiply parentheses

3x-3

Back to the equation:

-(3x-3)


We add all the numbers together, and all the variables

-5x^2+17x-(3x-3)+7=0

We get rid of parentheses

-5x^2+17x-3x+3+7=0

We add all the numbers together, and all the variables

-5x^2+14x+10=0

a = -5; b = 14; c = +10;
Δ = b2-4ac
Δ = 142-4·(-5)·10
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{11}}{2*-5}=\frac{-14-6\sqrt{11}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{11}}{2*-5}=\frac{-14+6\sqrt{11}}{-10}
$