7x(4x-9)=-26+6x

Solution for 7x(4x-9)=-26+6x equation:

7x(4x-9)=-26+6x

We move all terms to the left:

7x(4x-9)-(-26+6x)=0

We add all the numbers together, and all the variables

7x(4x-9)-(6x-26)=0

We multiply parentheses

28x^2-63x-(6x-26)=0

We get rid of parentheses

28x^2-63x-6x+26=0

We add all the numbers together, and all the variables

28x^2-69x+26=0

a = 28; b = -69; c = +26;
Δ = b2-4ac
Δ = -692-4·28·26
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-43}{2*28}=\frac{26}{56}
=13/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+43}{2*28}=\frac{112}{56}
=2
$