5x(5x-8)=4x(3x+7)

Solution for 5x(5x-8)=4x(3x+7) equation:

5x(5x-8)=4x(3x+7)

We move all terms to the left:

5x(5x-8)-(4x(3x+7))=0

We multiply parentheses

25x^2-40x-(4x(3x+7))=0


We calculate terms in parentheses: -(4x(3x+7)), so:

4x(3x+7)

We multiply parentheses

12x^2+28x

Back to the equation:

-(12x^2+28x)


We get rid of parentheses

25x^2-12x^2-40x-28x=0

We add all the numbers together, and all the variables

13x^2-68x=0

a = 13; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·13·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*13}=\frac{0}{26}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*13}=\frac{136}{26}
=5+3/13
$