(x-4)(x+5)=10x-3

Solution for (x-4)(x+5)=10x-3 equation:

(x-4)(x+5)=10x-3

We move all terms to the left:

(x-4)(x+5)-(10x-3)=0

We get rid of parentheses

(x-4)(x+5)-10x+3=0

We multiply parentheses ..

(+x^2+5x-4x-20)-10x+3=0

We get rid of parentheses

x^2+5x-4x-10x-20+3=0

We add all the numbers together, and all the variables

x^2-9x-17=0

a = 1; b = -9; c = -17;
Δ = b2-4ac
Δ = -92-4·1·(-17)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{149}}{2*1}=\frac{9-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{149}}{2*1}=\frac{9+\sqrt{149}}{2}
$