5x^2-35x=35x-7

Solution for 5x^2-35x=35x-7 equation:

5x^2-35x=35x-7

We move all terms to the left:

5x^2-35x-(35x-7)=0

We get rid of parentheses

5x^2-35x-35x+7=0

We add all the numbers together, and all the variables

5x^2-70x+7=0

a = 5; b = -70; c = +7;
Δ = b2-4ac
Δ = -702-4·5·7
Δ = 4760
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:

$\sqrt{\Delta}=\sqrt{4760}=\sqrt{4*1190}=\sqrt{4}*\sqrt{1190}=2\sqrt{1190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1190}}{2*5}=\frac{70-2\sqrt{1190}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1190}}{2*5}=\frac{70+2\sqrt{1190}}{10}
$