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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-(5(x-7)x)+14=0


We calculate terms in parentheses: -(5(x-7)x), so:

5(x-7)x

We multiply parentheses

5x^2-35x

Back to the equation:

-(5x^2-35x)


We get rid of parentheses

-5x^2+2x+35x+14=0

We add all the numbers together, and all the variables

-5x^2+37x+14=0

a = -5; b = 37; c = +14;
Δ = b2-4ac
Δ = 372-4·(-5)·14
Δ = 1649
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{-(37)-\sqrt{1649}}{2*-5}=\frac{-37-\sqrt{1649}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{1649}}{2*-5}=\frac{-37+\sqrt{1649}}{-10}
$