7x^2-14x-5x+5=21x^2-14x+3

Solution for 7x^2-14x-5x+5=21x^2-14x+3 equation:

7x^2-14x-5x+5=21x^2-14x+3

We move all terms to the left:

7x^2-14x-5x+5-(21x^2-14x+3)=0

We add all the numbers together, and all the variables

7x^2-19x-(21x^2-14x+3)+5=0

We get rid of parentheses

7x^2-21x^2-19x+14x-3+5=0

We add all the numbers together, and all the variables

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

a = -14; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-14)·2
Δ = 137
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{-(-5)-\sqrt{137}}{2*-14}=\frac{5-\sqrt{137}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{137}}{2*-14}=\frac{5+\sqrt{137}}{-28}
$