-5(x-3)9x=35

Solution for -5(x-3)9x=35 equation:

-5(x-3)9x=35

We move all terms to the left:

-5(x-3)9x-(35)=0

We multiply parentheses

-45x^2+135x-35=0

a = -45; b = 135; c = -35;
Δ = b2-4ac
Δ = 1352-4·(-45)·(-35)
Δ = 11925
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:

$\sqrt{\Delta}=\sqrt{11925}=\sqrt{225*53}=\sqrt{225}*\sqrt{53}=15\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-15\sqrt{53}}{2*-45}=\frac{-135-15\sqrt{53}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+15\sqrt{53}}{2*-45}=\frac{-135+15\sqrt{53}}{-90}
$