4x-10=7x(x-10)

Solution for 4x-10=7x(x-10) equation:

4x-10=7x(x-10)

We move all terms to the left:

4x-10-(7x(x-10))=0


We calculate terms in parentheses: -(7x(x-10)), so:

7x(x-10)

We multiply parentheses

7x^2-70x

Back to the equation:

-(7x^2-70x)


We get rid of parentheses

-7x^2+4x+70x-10=0

We add all the numbers together, and all the variables

-7x^2+74x-10=0

a = -7; b = 74; c = -10;
Δ = b2-4ac
Δ = 742-4·(-7)·(-10)
Δ = 5196
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:

$\sqrt{\Delta}=\sqrt{5196}=\sqrt{4*1299}=\sqrt{4}*\sqrt{1299}=2\sqrt{1299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{1299}}{2*-7}=\frac{-74-2\sqrt{1299}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{1299}}{2*-7}=\frac{-74+2\sqrt{1299}}{-14}
$