4x(7x+8)=5x(9x-15)

Solution for 4x(7x+8)=5x(9x-15) equation:

4x(7x+8)=5x(9x-15)

We move all terms to the left:

4x(7x+8)-(5x(9x-15))=0

We multiply parentheses

28x^2+32x-(5x(9x-15))=0


We calculate terms in parentheses: -(5x(9x-15)), so:

5x(9x-15)

We multiply parentheses

45x^2-75x

Back to the equation:

-(45x^2-75x)


We get rid of parentheses

28x^2-45x^2+32x+75x=0

We add all the numbers together, and all the variables

-17x^2+107x=0

a = -17; b = 107; c = 0;
Δ = b2-4ac
Δ = 1072-4·(-17)·0
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(107)-107}{2*-17}=\frac{-214}{-34}
=6+5/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(107)+107}{2*-17}=\frac{0}{-34}
=0
$