10x(2x-14)=29x^2-100

Solution for 10x(2x-14)=29x^2-100 equation:

10x(2x-14)=29x^2-100

We move all terms to the left:

10x(2x-14)-(29x^2-100)=0

We multiply parentheses

20x^2-140x-(29x^2-100)=0

We get rid of parentheses

20x^2-29x^2-140x+100=0

We add all the numbers together, and all the variables

-9x^2-140x+100=0

a = -9; b = -140; c = +100;
Δ = b2-4ac
Δ = -1402-4·(-9)·100
Δ = 23200
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:

$\sqrt{\Delta}=\sqrt{23200}=\sqrt{400*58}=\sqrt{400}*\sqrt{58}=20\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-20\sqrt{58}}{2*-9}=\frac{140-20\sqrt{58}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+20\sqrt{58}}{2*-9}=\frac{140+20\sqrt{58}}{-18}
$